Find the sum of the following series:

1 + 4/7 + 9/49 + 16/343 + .......... to infinity

1 + 4/7 + 9/49 + 16/343 + ... can also be expressed as:

(2^1 - 1) / (7^0) + (2^2+0) / (7^1) + (2^3 +1) / (7^2) + ...

from here we can pretty easily see that when used Sin function to add -1, 0 or +1  we can express this series as:

Σ((2^n - Sin( nπ / 2)) / (7^(n-1)))

now when we sum all these from n=1 to n=∞ the series converges to 91/50 = 1.82 and thats it :)

Posted by atheron on 2006-03-11 13:19:56