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Let S=sum(r=1)^(117)(1)/(2[sqrtr]+1), wh...

Let `S=sum_(r=1)^(117)(1)/(2[sqrtr]+1)`, when `[*]` denites the greatest integer function and if `S=(p)/(q)`, when p and q are co-primes, the value of `p+q` is

A

20

B

76

C

19

D

69

Text Solution

Verified by Experts

The correct Answer is:
B
`:.S=sum_(r=1)^(117)(1)/(2[sqrtr]+1)`
`=(3)/(2*1+1)+(5)/(2*2+1)+(7)/(2*3+1)+"....."+(19)/(2*9+1)+(18)/(2*10+1)`
`=9+(18)/(21)=9+(6)/(7)=(69)/(7)`
`:. P=69` and `q=7 implies p+q=69+7=76`
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