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Since the

is a constant, the series convergences.

The sum to infinity

Let denote the term of the AP.

Since they are consecutive terms of a GP,

, thus its not convergent

Sum of first 3 terms

—(1)

Sum of last 3 terms ; Here we consider an AP that has first term and common difference .

—(2)

Sum of n terms =

—(3)

Solve for n.

(i) Volume,

Volume of kth later,

(ii)

Since $latex r = \frac{5}{9} <1, S_{\infty} $ exists. Theoretical Max Volume, $latex S_{\infty} = \frac{8800 \pi}{1 - \frac{5}{9}} = 19800 \pi$. Total Volume, $latex S_n = \frac{8800 \pi (1 - (\frac{5}{9})^n)}{1 - \frac{5}{9}}$ We want $latex S_n \le 0.95 S_{\infty}$

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