SOLUTION: Find the sum of the infinite series 1/(1 × 3 × 5)+1/(3 × 5 × 7)+1/(5 × 7 × 9)+1/(7 × 9 × 11)+ .......

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Question 780889: Find the sum of the infinite series
1/(1 × 3 × 5)+1/(3 × 5 × 7)+1/(5 × 7 × 9)+1/(7 × 9 × 11)+ .......
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
The series is:
+ ...

The n-th term of the series is given by
t%5Bn%5D=1%2F%28%282n-1%29%282n%2B1%29%282n%2B3%29%29




t%5Bn%5D=1%2F%284%282n%2B1%29%29-5%2F%288%282n%2B3%29%29%2B3%2F%288%282n-1%29%29

The sum of the given series up to infinity is given by


I have given you the clue. From here see if you can use your brain and proceed...