S(n) is a statement about positive integers n such that whenever S(k) is true, S(k + 1) must also be true. Furthermore, there exists some positive integer n0 such that S(n0) is not true. Of the following, which is the strongest conclusion that can be drawn?

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∻Solution by Steps∻ ‖ step 1 ⋮ To find the definite integral of $ x^4 $ from $ x = 3 $ to $ x = 5 $, we use the fundamental theorem of calculus. ‖ ‖ step 2 ⋮ The antiderivative of $ x^4 $ is $ \frac{x^5}{5} $ plus a constant. ‖ ‖ step 3 ⋮ We evaluate $ \frac{x^5}{5} $ at the upper limit of integration $ x = 5 $ and at the lower limit $ x = 3 $. ‖ ‖ step 4 ⋮ The definite integral is $ \left[\frac{5^5}{5}\right] - \left[\frac{3^5}{5}\right] $. ‖ ‖ step 5 ⋮ Simplifying, we get $ \frac{3125}{5} - \frac{243}{5} $. ‖ ‖ step 6 ⋮ The result is $ \frac{2882}{5} $, which can also be written as 576.4. ‖ ∻Answer∻ ⚹ The definite integral of $ x^4 $ from $ x = 3 $ to $ x = 5 $ is $ \frac{2882}{5} $ or 576.4. ⚹ ∻Key Concept∻ ⚹Definite Integral of a Polynomial Function⚹ ∻Explanation∻ ⚹The definite integral of a polynomial function $ x^n $ from $ a $ to $ b $ is found by evaluating the antiderivative $ \frac{x^{n+1}}{n+1} $ at $ b $ and $ a $ and then subtracting the two results.⚹◊What is the significance of the statement S(n) in terms of⍭ Generate me a similar question◊

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