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The following sequence forms a convergent geometric sequence: $5x ; x^{2} ; \frac{x^{3}}{5} ; ...$

1. Determine the possible values of $x$
2. If $x=2$, calculate $S_{\infty}$
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## 1 Answer

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1. -1< x^2/5x<1

-1<x/5<1

-5<x<5

2. r= 2^2/5(2) = 2/5

a= 5(2)= 10

sum = 10/(1- 2/5)

= 16.67
by Diamond (44,680 points)

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