Question

The sum of the terms of an infinitely decreasing G.P. is $S$. The sum of the squares of the terms of the progression is -

• A. $\frac{S}{2S-1}$
• B. $\frac{S^2}{2S-1}$
• C. $\frac{S}{2-S}$
• D. $S^2$

Answer 1

Answer: (B)

$\frac{S^2}{2S-1}$

$1,r,r^2,r^3..........,(r<0)$

$S_{\infty }=\frac{a}{1-r}$

$S=\frac{1}{1-r}$

$r=1-\frac{1}{S}=\frac{S-1}{S}$

$S_{\infty }=1^2+r^2+r^4+r^6+..........$

$S_{\infty }=\frac{1}{1-r^2}$

$=\frac{1}{1-{\left(\frac{S-1}{S}\right)}^2}$

$=\frac{S^2}{S^2-S^2-1+2S}$

$=\frac{S^2}{2S-1}$