In each part, use a CAS to find the sum of the series if itconverges, and then confirm

Chapter 9, Problem 40

(choose chapter or problem)

In each part, use a CAS to find the sum of the series if it converges, and then confirm the result by hand calculation.

(a) $\sum_{k=1}^{\infty}(-1)^{k+1} 2^{k} 3^{2-k}$

(b) $\sum_{k=1}^{\infty} \frac{3^{3 k}}{5^{k-1}}$

Equation Transcription:

$\sum\limits_{k=1}^{\infty{}}(-1{)}^{k+1}{2}^{k}{3}^{2-k}$

$\sum\limits_{k=1}^{\infty{}}\frac{{3}^{3k}}{{5}^{k-1}}$

$\sum\limits_{k=1}^{\infty{}}\frac{1}{4{k}^{2}-1}$

Text Transcription:

sum_k=1^infinity (-1)^k+1 2^k 3^2-k

sum_k=1^infinity3^3k/5^k-1

sum_k=1^infinity 1/4k^2-1

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