Find the sum of the following series:
1 + 4/7 + 9/49 + 16/343 + .......... to infinity
x = 1 + 4/7 + 9/49 + 16/343 + ...
multiply by 7:
7x = 7 + 4 + 9/7 + 16/49 + 25/343 + ...
subtract:
6x = 10 + 5/7 + 7/49 + 9/343 + ...
multiply by 7:
42x = 70 + 5 + 7/7 + 9/49 + 11/343 + ...
subtract:
36x = 65 + 2/7 + 2/49 + 2/343 + ...
multiply by 7:
252x = 525 + 2 + 2/7 + 2/49 + 2/343 + ...
subtract:
216x = 462
divide:
x = 462/216 = 77/36

Posted by Charlie
on 20060311 09:17:49 