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

Question

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

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

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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`

4 views Answered 2023-02-05 15:29