`(1)/(log_(2)N)+(1)/(log_(3)N)+(1)/(log_(4)N)+...+(1)/(log_(100)N)` किसके बराबर है, `(N!=1)` ?

Options

A. `(1)/(log_(100!)N)`
B. `(1)/(log_(99!)N)`
C. `(99)/(log_(100!)N)`
D. `(99)/(log_(99!)N)`

Answer

A

Explanation

दिया है ,
` 1/(log_(2)N) + 1/(log_(4)N) + 1/(log_(4)N) +......+1/(log_(100)N) `
` = log_(N) 2 + log_(N) 3 + log_(n) 4 + .....+ log_(N) 100`
`[:' log_(a)b = 1/(log_(b) a)]`
` = log_(N) (2*3*4*.....100)`
` = log_(N) (100)!`
`[:' n(n-1)(n-2).......3*2*1*=n!]`
` = 1/(log_((100)!)N)`