sum it up

Algebra Level 3

1/(3^2-1)+1/(5^2-1)+1/(7^2-1)+........1/(35^2-1)=?

17/72 19/72 4/17 21/36

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1 solution

Gaurav Singh
Jun 5, 2015

Each term can be written as the difference between two and when all of them are added most of them gets cancelled and the remaining we just add to get the answer.....each term can be written as 1/2(1/(n+1)-1/(n-1)) so it becomes 1/2(1/4-1/2)+1/2(1/6-1/4).......1/2(1/36-1/34) this finally becomes 1/4-1/72 which equals to 17/72

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