Chapter 9, Problem 12PS

(a)

To determine

To calculate: The first five terms of the sequence ${\displaystyle \sum _{n=1}^{\infty }\frac{1}{2^{n+{\left(-1\right)}^n}}}$ of partial sums.

(b)

To determine

To prove: That the ratio test is inconclusive for the series ${\displaystyle \sum _{n=1}^{\infty }\frac{1}{2^{n+{\left(-1\right)}^n}}}$.

(c)

To determine

Whether the provided series ${\displaystyle \sum _{n=1}^{\infty }\frac{1}{2^{n+{\left(-1\right)}^n}}}$ is convergent or divergent.