Question

s is the sum to infinite terms of a G.P. whose first term is 1. Then the sum of n term is

• A. $s(1-{(1-\frac{1}{s})}^n)$
• B. $\frac{1}{s}(1-{(1-\frac{1}{s})}^n)$
• C. $1-{(1-\frac{1}{s})}^n$
• D. $1+{(1-\frac{1}{s})}^n$

Answer 1

The correct option is A $s(1-{(1-\frac{1}{s})}^n)$

This question is based on the concept of geometric series.
sum to infinite terms of a $G.P=s=\frac{1}{1-r}$
and sum to n terms of a $G.P=S_n$ = $a\ast \frac{(r^n-1)}{(r-1)}$
now substituting r from first equation in second equation, we get
$S_n=\frac{1[1-{\left(\frac{s-1}{s}\right)}^n]}{1-\left(\frac{s-1}{s}\right)}=s(1-{(1-\frac{1}{s})}^n)$
Hence, option A is correct.