Question

what is the sum of infinite G.P. 14+(-2)+(2/7)+(-2/49)+...........?​

Answer 1

please see the attachment

Answer 2

The sum of infinite G.P is $S_{\infty}=\frac{49}{4}$

Step-by-step explanation:

Given : Geometric sequence $14+(-2)+(\frac{2}{7})+(-\frac{2}{49})+.......$

To find : What is the sum of infinite G.P.?

Solution :

In Geometric sequence $14+(-2)+(\frac{2}{7})+(-\frac{2}{49})+.......$

The first term is a=14.

The common ratio is $r=\frac{-2}{14}=-\frac{1}{7}$

The sum of infinite G.P formula is $S_{\infty}=\frac{a}{1-r}$

$S_{\infty}=\frac{14}{1-(-\frac{1}{7})}$

$S_{\infty}=\frac{14}{1+\frac{1}{7}}$

$S_{\infty}=\frac{14}{\frac{8}{7}}$

$S_{\infty}=\frac{98}{8}$

$S_{\infty}=\frac{49}{4}$

Therefore, the sum of infinite G.P is $S_{\infty}=\frac{49}{4}$

#Learn more

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