Question

Find the sum of G.P. :

`1 - 1/3 + 1/3^2 - 1/3^3 + .........` to n terms.

Answer 1

Given G.P. : `1 - 1/3 + 1/3^2 - 1/3^3 + .........` upto n terms

Here,

First term, a = 1

Common ratio, r = `(-1/3)/1 = -1/3`   ...(∵ r < 1)

Number of terms to be added = n

∴ `S_n = (a(1 - r^n))/(1 - r)`

`=> S_n = (1(1 - (-1/3)^n))/(1 - (-1/3))`

= `(1(1 - (-1/3)^n))/(1 + 1/3)`

= `[1 - (-1/3)^n]/(4/3)`

= `3/4[1 - (-1/3)^n]`