# Chapter 11 - Infinite Series - 11.2 Summing and Infinite Series - Exercises - Page 548: 43

(a) Geometric (b) Not geometric (c) Not geometric (d) Geometric

#### Work Step by Step

(a) Given $$\sum_{n=0}^{\infty} \frac{7^{n}}{29^{n}}$$ This is a geometric series for $c=1$ and $r=\frac{7}{29}$ (b) Given $$\sum_{n=3}^{\infty} \frac{1}{n^{4}}$$ This is not a geometric series because here we can not find the common ratio. (c) Given $$\sum_{n=0}^{\infty} \frac{n^{2}}{2^{n}}$$ This is not a geometric series because have we can not find the common ratio. (d) Given$$\sum_{n=5} \pi^{-n}$$ The given series can be written as $$\sum_{n=5}^{\infty} \frac{1}{\pi^{n}}=\frac{1}{\pi^{5}}+\frac{1}{\pi^{6}}+\frac{1}{\pi^{7}}+\ldots . .$$ Which is a geometric series with $C=\frac{1}{\pi^{5}}$ and $r=\frac{1}{\pi}$

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