SOLUTION: 1/15+1/35+1/63+1/99+1/143/+1/199=

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Question 1121014: 1/15+1/35+1/63+1/99+1/143/+1/199=
Found 2 solutions by greenestamps, Alan3354:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


I suspect the last fraction is typed incorrectly. 1/195 would make a much nicer problem. I will solve the problem using 1/195 instead of 1/199.

The series can be written as



Each term can be written in the form 1%2F%28%28n-1%29%28n%2B1%29%29.

Decomposing that fraction shows each term can be written in the form

%281%2F2%29%28%281%2F%28n-1%29-1%2F%28n%2B1%29%29%29

Then the sum is


or
%281%2F2%29%281%2F3-1%2F15%29
which is
%281%2F2%29%284%2F15%29+=+2%2F15

If the last fraction is really 1/199, then treat that last fraction separately; the sum will be

%281%2F2%29%281%2F3-1%2F13%29%2B1%2F199

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1/15+1/35+1/63+1/99+1/143/+1/199
----
= 7/105+3/105 + 1/63+1/99+1/143/+1/199
= 2/21 + 1/63+1/99+1/143/+1/199
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Combine the terms 2 at a time.
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If the last term should be 1/195, a different approach can be used, but it's not my job to figure out what you might have meant.