Question

Find the sum of the series $1+2+4+...$ upto $9$ terms. (Using the formula)

Answer 1

Given series is $1+2+4+$ ____upto $9$ terms

Here $a=1,r=\frac{2}{1}=\frac{4}{2}=2$
and $n=9$
We know, $S_n=a\left[\frac{r^n-1}{r-1}\right],r>1$
$=1\left[\frac{2^9-1}{2-1}\right]$
$=\frac{256-1}{1}=255$

Therefore, the sum of the series is $255$.