Test choice explained.
AskSia identifies which test fits the series's structure and explains why before applying it. (AskSiaは、どのテストが級数の構造に適合するかを特定し、適用する前にその理由を説明します。)
Method-aware
JA
Series Solver
Series convergence, the right test for each one. (級数の収束、それぞれに適切なテスト。)
Type or photograph the series. AskSia picks the most efficient convergence test (ratio, root, comparison, limit comparison, integral, alternating, or p-series) and shows the test conditions and conclusion clearly. Power series radius and interval of convergence supported. (シリーズを入力または撮影してください。AskSiaは最も効率的な収束テスト（比率、根、比較、極限比較、積分、交項、またはp級数）を選択し、テスト条件と結論を明確に示します。べき級数の半径と収束区間がサポートされています。)
Works with word problems, equations, code, and science prompts.
∫ 3x² · sin(x) dx
SubjectsCalculusAlgebraPhysicsChemistryBiologyCSStatisticsEcon
4.9 / 5 · trusted by 2M+ students · 50M+ problems solved
asksia.ai/solver
98% · Verified
Problem
Find the area enclosed between y = x² and y = 2x in the first quadrant.
1
Find the points of intersection
Set the curves equal: x² = 2x → x(x - 2) = 0, so x = 0 and x = 2.
2
Identify which curve is on top
On (0, 2), 2x > x², so y = 2x is the upper curve.
3
Set up the area integral
A = ∫₀² (2x - x²) dx
4
Integrate term-by-term
A = [ x² - x³/3 ]₀²
Final Answer
A = 4/3 sq. units
Quick Answer
How do you test a series for convergence? (級数の収束をテストするにはどうすればよいですか？)
To test a series for convergence, look at the terms. If they do not approach zero, the series diverges (divergence test). For positive-term series, try the ratio or root test for factorials and exponentials, the p-series rule for 1/n^p, the integral test for terms matching a continuous decreasing function, or comparison with a known series. For alternating series, the alternating series test applies if terms decrease to zero. Each test has conditions and a conclusion; pick the one whose conditions are easiest to verify. (級数の収束をテストするには、項を見ます。項がゼロに近づかない場合、級数は発散します（発散テスト）。正項級数の場合、階乗と指数関数には比率または根テスト、1/n^pにはp級数ルール、連続減少関数に一致する項には積分テスト、または既知の級数との比較を試します。交項級数の場合、項がゼロに減少する場合、交項級数テストが適用されます。各テストには条件と結論があります。条件を検証するのが最も簡単なものを選びます。)
98%
solution accuracy
50M+
problems solved
~1.5s
avg solve time
A+
study-ready explanations
Why AskSia Solver
Why students use AskSia for Series. (学生がSeriesにAskSiaを使用する理由。)
Every step transparent, every answer self-checked. (すべてのステップが透明で、すべての回答が自己チェックされています。)
Ratio and root tests.
For factorials and exponentials, AskSia computes the limit of |a_(n+1)/a_n| or the n-th root and applies the conclusion. (階乗と指数関数について、AskSiaは|a_(n+1)/a_n|の極限またはn乗根を計算し、結論を適用します。)
Ratio/root
Comparison tests.
AskSia picks a benchmark series and compares term by term, using direct or limit comparison. (AskSiaはベンチマーク級数を選択し、直接比較または極限比較を使用して項ごとに比較します。)
Comparison
Power series.
Radius and interval of convergence found via the ratio test, with endpoint checks for inclusion. (べき級数。半径と収束区間は比率テストを介して見つけられ、区間を含めるための端点チェックが行われます。)
Power series
Photo, paste, or type.
Snap handwritten or printed problems with your phone, paste from any online homework portal, or type with full LaTeX support. (電話で手書きまたは印刷された問題をスナップするか、オンラインの宿題ポータルから貼り付けるか、完全なLaTeXサポートで入力します。)
Multi-modal input
Verified by AskSia.
Every answer gets a self-check pass. Sia catches sign errors and algebra mistakes before you submit your homework. (すべての回答にはセルフチェックパスがあります。Siaは、宿題を提出する前に符号エラーと代数ミスを検出します。)
Self-checked
How It Works
Solve any Series problem in three steps. (3つのステップで任意のSeries問題を解決します。)
Step 01
Enter the problem.
Type the expression, paste from your homework, snap a photo, or speak it. AskSia parses your input and identifies the structure. (式を入力するか、宿題から貼り付けるか、写真を撮るか、話します。AskSiaは入力を解析し、構造を特定します。)
Input mode
Snap a Photo
Textbook, handwriting, screenshot
Paste Text
Word problem or equation
Calculator
LaTeX-ready equation editor
Step 02
AskSia picks the method.
Based on the problem structure, AskSia chooses the cleanest solution path and labels each step with the operation performed. (問題構造に基づき、AskSiaは最もクリーンな解法パスを選択し、各ステップに実行された操作をラベル付けします。)
1
Set curves equal
x² = 2x → x = 0, x = 2
2
Set up the integral
A = ∫₀² (2x - x²) dx
3
Evaluate
A = [x² - x³/3]₀² = 4/3
Step 03
Read the verified answer.
Final result appears with a substitution or composition check. Practice problems on the same concept are one tap away. (最終結果は、代入または合成チェックとともに表示されます。同じ概念の練習問題はワンタップで利用できます。)
Auto-generated diagram
Region between y = 2x and y = x² — area = 4/3
Available On
Solve anywhere
you study.
Every solve syncs across Web, iOS, and Android — start it at your desk, finish on your phone.
Web App
Full study studio
Split-panel interface with the worked solution on the left, the auto-generated diagram and AI tutor chat on the right.
Drag & drop image upload + LaTeX equation editor
Auto-generated diagrams render alongside steps
Side-panel AI tutor chat for hints and alt methods
Export to PDF, DOCX, Notion, or Google Docs
Hi! What are we studying today?
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Calculus
98% verified
1.4s
Step 4 of 4 · Evaluate
A = [x² - x³/3]₀² = 4/3
Mobile App
Snap & solve, anywhere
Open the camera, frame the problem, and the worked solution plus diagram appear in seconds.
One-tap snap-and-solve on iOS and Android
Pinch-to-zoom diagrams, swipe between steps
Auto-sync solves with your Web library
Offline review of saved solutions and flashcards
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AskSia
+What can I do for you?
Homework solver
Live transcribe
File summary
Snap
YouTube
Flashcard
Calc
98%
1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
What the Series solver covers. (Seriesソルバーがカバーするもの。)
p-series.
1/n^p converges if p > 1, diverges otherwise. AskSia applies the rule directly. (p級数。1/n^pはp > 1の場合に収束し、それ以外の場合は発散します。AskSiaはルールを直接適用します。)
p-series
Geometric series.
sum a*r^n converges if |r| < 1, with sum a/(1-r). AskSia identifies and applies. (等比級数。sum a*r^nは|r| < 1の場合に収束し、和はa/(1-r)になります。AskSiaはこれを識別して適用します。)
Geometric
Ratio test.
Series with factorials like sum n!/n^n. AskSia computes the ratio limit. (比率テスト。sum n!/n^nのような階乗を持つ級数。AskSiaは比率の極限を計算します。)
Factorials
Alternating series.
sum (-1)^n / n. Check decreasing terms approaching zero. (交項級数。sum (-1)^n / n。ゼロに近づく減少項を確認します。)
Alternating
Power series.
sum c_n * x^n. Radius of convergence by ratio test. (べき級数。sum c_n * x^n。比率テストによる収束半径。)
Power series
Verify your homework.
Paste your candidate answer and the original problem. AskSia walks the work, flags any divergent step, and tells you the correct final value. (宿題を確認します。候補となる回答と元の問題を貼り付けます。AskSiaは作業を追跡し、発散するステップにフラグを立て、正しい最終値を示します。)
Answer check
Compare
AskSia vs. ChatGPT,
Photomath & Symbolab.
General chatbots hallucinate. Photo solvers stop at math. AskSia is built for actual coursework with verified accuracy, visual learning, and every subject.
| Feature | AskSia Solver | ChatGPT | Photo Solvers |
|---|---|---|---|
| Solution accuracy | ✓ 98% | ~70-85%, hallucinations | ~90%, math only |
| Auto-generated diagrams | ✓ Every solve | Inconsistent / broken | Graphs only, math-only |
| Step-by-step explanations | ✓ Numbered + plain English | Inconsistent depth | ✓ Math steps |
| Subject coverage | ✓ Math, Physics, Chem, Bio, CS, Econ | ✓ Wide but unverified | Math only |
| Photo input | ✓ Handwriting + diagrams + code | Photos OK, weak on handwriting | ✓ Math photos only |
| Answer verification | ✓ Self-checked before display | No verification | Math engine only |
| Tutor follow-ups | ✓ Hints, alt methods, ELI5 | ✓ General chat | Not available |
| Practice and flashcards | ✓ One-tap from any solve | Manual prompting | Not available |
| Code debugging | ✓ Python, Java, C++, SQL... | ✓ Yes | Not available |
| Free to start | ✓ Daily solves, no card | Limited model access | Steps locked behind paywall |
FAQ
Frequently asked questions. (よくある質問。)
Which convergence test does AskSia try first?
It looks at structure. Factorials or n-th powers trigger the ratio or root test. Forms like 1/n^p trigger the p-series test. Alternating signs trigger the alternating series test. If none match obviously, AskSia uses limit comparison with a known series. The chosen test is named at the top of the output. (構造を見ます。階乗またはn乗は比率または根テストをトリガーします。1/n^pのような形式はp級数テストをトリガーします。交互の符号は交互級数テストをトリガーします。明らかに一致するものがない場合、AskSiaは既知の級数との極限比較を使用します。選択されたテストは出力の上部に名前が付けられています。)
Can AskSia find the radius of convergence?
Yes. For a power series sum c_n * x^n, AskSia applies the ratio test with x as a parameter and finds the values of x for which the limit is less than 1. This gives the radius R, and AskSia then checks the endpoints x = +R and x = -R separately to determine the full interval of convergence. (はい。べき級数 sum c_n * x^n の場合、AskSiaはxをパラメータとして比率テストを適用し、極限が1未満になるxの値を見つけます。これにより半径Rが得られ、AskSiaは端点x = +Rおよびx = -Rを個別にチェックして、完全な収束区間を決定します。)
What is the difference between conditional and absolute convergence?
A series converges absolutely if the sum of absolute values of its terms converges. It converges conditionally if it converges but the sum of absolute values diverges. The alternating harmonic series is the classic example of conditional convergence. AskSia checks absolute convergence first, then applies the alternating series test if needed. (級数は、項の絶対値の合計が収束する場合、絶対収束します。級数が収束し、項の絶対値の合計が発散する場合、条件付き収束します。交互調和級数は、条件付き収束の古典的な例です。AskSiaはまず絶対収束をチェックし、必要に応じて交互級数テストを適用します。)
Does AskSia show the limit computation?
Yes. For the ratio test, the limit of |a_(n+1)/a_n| as n approaches infinity is computed step by step, often using L'Hopital or algebraic simplification. The numerical value (or +/- infinity) determines the conclusion. AskSia shows the limit setup, the manipulation, and the final number alongside the test's verdict. (はい。比率テストの場合、nが無限大に近づくにつれて|a_(n+1)/a_n|の極限は、ロピタルの定理または代数的簡略化を使用して、段階的に計算されます。数値（または+/-無限大）が結論を決定します。AskSiaは、テストの評決とともに、極限の設定、操作、および最終的な数値を示します。)
How accurate is AskSia?
AskSia hits 98% accuracy on standard high school and college coursework, measurably higher than ChatGPT, Photomath, and Symbolab on the same problem sets. Accuracy comes from subject-specialized models, a symbolic verification pass that catches arithmetic errors, and a self-check step that re-derives the answer before showing it to you. (AskSiaは、標準的な高校および大学のコースワークで98%の精度を達成しており、同じ問題セットでChatGPT、Photomath、Symbolabよりも測定可能に高くなっています。精度は、対象分野に特化したモデル、算術エラーを検出する記号検証パス、および回答を表示する前に再導出するセルフチェックステップから得られます。)
Can I get practice problems and flashcards?
Yes. After any solve, ask Sia to generate similar practice problems at SAT, ACT, AP, IB, or college difficulty, or build a flashcard set on the underlying concept in one tap. Useful for exam prep and spaced repetition before a quiz, midterm, or final. (はい。どの問題も解決した後、SiaにSAT、ACT、AP、IB、または大学レベルの難易度で同様の練習問題を生成するように依頼するか、ワンタップで根本的な概念に関するフラッシュカードセットを作成します。クイズ、中間試験、または期末試験前の試験準備と間隔反復に役立ちます。)
How much does AskSia cost?
AskSia has a free plan that includes daily solves across all subjects. AskSia Pro and Super include unlimited solves, advanced subjects, the full AI tutor companion, exports, and priority response speed. See pricing for details. (AskSiaには、すべての科目で毎日解決できる無料プランがあります。AskSia ProおよびSuperには、無制限の解決、高度な科目、完全なAIチューターコンパニオン、エクスポート、および優先応答速度が含まれます。詳細については、価格設定を参照してください。)
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Convergence or divergence, with the test that proves it. (収束または発散、それを証明するテストとともに。)
Join 2M+ students using AskSia to solve series problems step-by-step. Photo input, plain-English explanations, and a verification check on every solve. (AskSiaを使用して段階的にシリーズ問題を解決している200万人以上の学生に参加してください。写真入力、平易な英語の説明、およびすべての解決策に対する検証チェック。)