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8 years, 7 months ago
8 years, 1 month ago
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.