Question

Find the sum of G.P. :

`sqrt(3) + 1/sqrt(3) + 1/(3sqrt(3)) + ..........` to n terms. 

Answer 1

Given G.P. : `sqrt(3) + 1/sqrt(3) + 1/(3sqrt(3)) + ..........` upto n terms
Here,

First term, a = `sqrt(3)`

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

Number of terms to be added = n

∴ `S_n = (a(1 - r^n))/(1 - r)`

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

= `(sqrt(3)(1 - 1/3^n))/(2/3)`

= `(3sqrt(3))/2(1 - 1/3^n)`