What is the sum of infinite series 1+(4/7)+(9/7^2)+(16/7^3)+(25/7^4)+•••••••

Hi,

Let S = 1 + (4/7) + (9/7^2) + (16/7^3) + (25/7^3) +  .......

=> S/7 = 1/7 + (4/7^2) + (9/7^3) + (16/7^4) + (25/7^4) +  .......

Subtracting 2nd from 1st we get,

6S/7 = 1 + (3/7) + (5/7^2) + (7/7^3) + (9/7^3) +  .......

Again dividing by 7 we get

6S/7^2 = 1/7 + (3/7^2) + (5/7^3) + (7/7^4) + (9/7^5) +  .......

Again subtracting this from the above eqn we get,

36S/7^2 = 1 + (2/7) + (2/7^2) + (2/7^3) + (2/7^3) +  .......

Now the whole equation can be solved using the infinite GP formula.

Hope this answers your query.