Find the sum of the following series:
1 + 4/7 + 9/49 + 16/343 + .......... to infinity
(In reply to
solution by Charlie)
Corrected numbers in bold:
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 = 455 + 2 + 2/7 + 2/49 + 2/343 + ...
subtract:
216x = 392
divide:
x = 392/216 = 49/27
Edited on March 11, 2006, 2:27 pm
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Posted by Charlie
on 2006-03-11 14:26:55 |
re: solution -- corrected
