SOLUTION: find the partial fraction decomposition for 2/(x(x+2)) and use the result to find the following sum 2/(1*3) + 2/(3*5) + 2/(5*7) + ... + 2/(99*101)

SOLUTION: find the partial fraction decomposition for 2/(x(x+2)) and use the result to find the following sum 2/(13) + 2/(35) + 2/(57) + ... + 2/(99101)

Question 1117401: find the partial fraction decomposition for 2/(x(x+2)) and use the result to find the following sum
2/(1*3) + 2/(3*5) + 2/(5*7) + ... + 2/(99*101)
Answer by ikleyn(52915) (Show Source): You can put this solution on YOUR website!
.

 =  - .


So, 


    +  +   + ...   +  = 


=  +  +  + . . . +  = 


= all intermediate terms cancel each other, which leaves =  = .

Solved.

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These tricks are very well known. See the lesson
- Calculations with fractions
in this site.

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