Find the sum of infinite series `(1)/(1xx3xx5)+(1)/(3xx5xx7)+(1)/(5xx7 – InterviewSolution

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1.	Find the sum of infinite series `(1)/(1xx3xx5)+(1)/(3xx5xx7)+(1)/(5xx7xx9)+….`
Answer» Correct Answer - `1/(12)` `T_(r)=1/((2r-1)(2r+1)(2r+3))` `=1/4cdot((2r+3)-(2r-1))/((2r-1)(2r+1)(2r+3))` `=1/4[1/((2r-1)(2r+1))-1/((2r+1)(2r+3))]` `=1/4[V(r-1)-V(r )],` where V( r)=`1/((2r+1)(2r+3))` `thereforesum_(r=1)^(n)T_(r)=sum_(r=1)^(n)1/4[V(r-1)-V(r )]` `=1/4[V(0)-V(n)]` `=1/4[1/3-1/((2n+1)(2n+3))]` `therefore` Sum of infinite terms=`1/4[1/3-0]=1/12`

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