Determine the convergence of an infinite series using the Ratio Test.

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Convergence of a Series with Polynomial and Exponential Terms

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Determine whether \( \sum_{n=1}^{\infty} n\left(\frac{3}{4}\right)^n \) converges.

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Tests the ability to correctly apply the Ratio Test and evaluate limits of sequences involving algebraic and exponential expressions.

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