Question

Find the sum of G.P. :

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

Answer 1

Given G.P. : 0.3 + 0.03 + 0.003 + 0.003 + ...........

Here,

First term, a = 0.3

Common ratio, r = `0.03/0.3`= 0.1  ...(∵ r < 1)

Number of terms to be added, n = 8

∴ `S_n = (a(1 - r^n))/(1 - r)`

`=> S_8 = (0.3(1-(0.1)^8))/(1-0.1)`

= `(0.3(1 - (0.1)^8))/0.9`

=`(1 - (0.1)^8)/3`

= `1/3(1 - 1/10^8)`