Question

Find the sum to indicated number of terms in the geometric progression given:
$0.15,0.015,0.0015,.....20$ terms

Answer 1

$a=0.15,r=0.1,m=20$

$\therefore S=\frac{a(1-r^n)}{(1-r)}$

$=\frac{\left(0.15\right)(1-(0.1{)}^{20})}{(1-0.1)}$

$=\frac{0.15}{0.9}(1-{10}^{-20})$

$=\frac{0.15}{0.9}=\frac{15}{90}$

$=\frac{1}{6}$