Find the sum to `n`terms of the series: `1/(1. 3)+1/(3. 5)+1/(5. 7)+`A. `(1)/(2n+1)`B. `(2n)/(2n+1)`C. `(n)/(2n+1)`D. `(2n)/(n+1)`

Find the sum to `n`terms of the series: `1/(1. 3)+1/(3. 5)+1/(5. 7)+`A

1.	Find the sum to `n`terms of the series: `1/(1. 3)+1/(3. 5)+1/(5. 7)+`A. `(1)/(2n+1)`B. `(2n)/(2n+1)`C. `(n)/(2n+1)`D. `(2n)/(n+1)`
Answer» Correct Answer - C Let `T_(r)" be the "r^(th)` term of the given series. Then, `T_(r)=(1)/((2r-1)(2r+1)),r=1,2,3, . . .n` `rArr" "T_(r)=(1)/(2)((1)/(2r-1)-(1)/(2r+1))` Let S be the required sum. Then, `S=underset(r-1)overset(n)sumT_(r)` `S=(1)/(2){:[((1)/(1)-(1)/(3))+((1)/(3)-(1)/(5))+((1)/(5)-(1)/(7))+ . . . +((1)/(2n-1)-(1)/(2n+1))]:}` `rArr" "S=(1)/(2){1-(1)/(2n+1)}=(n)/(2n+1)`

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Find the sum to `n`terms of the series: `1/(1. 3)+1/(3. 5)+1/(5. 7)+`A. `(1)/(2n+1)`B. `(2n)/(2n+1)`C. `(n)/(2n+1)`D. `(2n)/(n+1)`

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