Question

Find sum of $\frac{1}{2},\frac{1}{3},\frac{2}{9}....$ upto $7$ terms.

Answer 1

Number of terms $n=7$
First term $=a=\frac{1}{2}$
Common ratio $=r=\frac{2}{3}$
Formula for sum of $n$ terms of G .P is given by

$S_n=\frac{a(r^n-1)}{r-1}$
$S_7=\frac{\left(\frac{1}{2}\right)[{\left(\frac{2}{3}\right)}^7-1]}{\frac{2}{3}-1}$
$S_6=\frac{3}{2}-{\left(\frac{2}{3}\right)}^6$

$S_6=\frac{2059}{1458}$