Question

Find the sum of G.P. :

`1 - 1/2 + 1/4 - 1/8 + ..........` to 9 terms. 

Answer 1

Given G.P. : `1 - 1/2 + 1/4 - 1/8 + ..........`

Here,

First term, a = 1

Common ratio, r = `(-1/2)/1 = -1/2`   ...(∵ r < 1)

Number of terms to be added, n = 9

∴ `S_n = (a(1 - r^n))/(1 - r)`

`=> S_8 = (1(1 - (-1/2)^9))/(1 - (-1/2))`

= `(1 - (-1/2)^9)/(1 + 1/2)`

= `(1 + 1/2^9)/(3/2)`

= `2/3(1 + 1/2^9)`

= `2/3(1 + 1/512)`

= `2/3 xx 513/512`

= `171/256`