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^(n1)))
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 20060311 13:19:56 