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Find the sum to `n`terms of the series: `1/(1. 3)+1/(3. 5)+1/(5. 7)+` |
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Answer» `S=1/(1*3)+1/(3*5)+1/(5*7)+...+n^(th)`term `S=sum_(r=1)^n 1/(r(r+2))` `S=sum_(r=1)^n((r+2-r)/(r(r+2)))` `S=1/2{sum_(r=1)^n(1/r-1/(r+2))}` `S=1/2{1+1/2-1/(n+1)-11/(n+2)}`. |
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