Determine the convergence of an infinite series involving a polynomial and an exponential using the ratio test.

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Convergence of n^2/e^n Using the Ratio Test

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Determine whether \(\sum_{n=1}^{\infty} \frac{n^2}{e^n}\) is convergent.

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Tests the ability to apply the ratio test, simplify algebraic expressions involving factorials or exponentials, and evaluate limits at infinity.

This is a standard problem in a Calculus II course when introducing tests for convergence of infinite series.