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Question
Find the sum of G.P. :
`sqrt(3) + 1/sqrt(3) + 1/(3sqrt(3)) + ..........` to n terms.
Solution
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)`
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