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If S(n) = 1/(6*11)+1/(11*16)+1/(16*21)+....

If `S_(n) = 1/(6*11)+1/(11*16)+1/(16*21)+...` upto n terms , then `6S_(n)` equals

A

`(5n-4)/(5n+6)`

B

`n/(5n+6)`

C

`(2n-1)/(5n+6)`

D

`1/(5n+6)`

Text Solution

Verified by Experts

The correct Answer is:
b
Let `S_(n) = 1/5 (1/6 - 1/11+1/(11) -1/(16) +...+ 1/(5n+1) -1/(5n+6))`
` = 1/5 (1/6 - 1/(5n+6))= n/(6(5n+6)) rArr 6S_(n) = n/(5n+6)`
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