Question

$0.3+0.03+0.003+0.0003+.......$ to $8$ terms.

Answer 1

0.3+0.03+0.003+0.0003+... to 8 terms.

given series is GP.

and sum of n terms of G.P. $=a\frac{1-r^h}{1-r}$

so have r = 0.01

so, sum $0.3\left(\frac{1.(0.1{)}^8}{1-\left(0.1\right)}\right)$

$=0.3\left(\frac{\mathrm{1.0.00000001}}{0.9}\right)$

$=0.3\left(\frac{0.99999998}{0.9}\right)$

$=0.3\left(\mathrm{1.1111110.9}\right)$

$=0.333333327$