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Sum to Infinity - 1 (Posted on 2006-03-11) Difficulty: 4 of 5
Find the sum of the following series:

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

No Solution Yet Submitted by Ravi Raja    
Rating: 3.7143 (7 votes)

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Solution solution | Comment 1 of 12

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 2006-03-11 09:17:49
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