`Lt_(ntooo) sum_(r=1)^(6n) 1/(n+r)=` (A) `log6` (B) `log7` (C) `log5` (D) `0`

sum_(r=1)^(n) 1/(log_(2^(r))4) is equal to

Given that lim_(nto oo) sum_(r=1)^(n) (log (r+n)-log n)/(n)=2(log 2-(1)/(2)) , lim_(n to oo) [(1)/(n^k)[(n+1)^k(n+2)^k.....(n+n)^k]]^(1//n) , is

If sum_(r=1)^n t_r= (n(n+1)(n+2))/3 then sum _(r=1)^oo 1/t_r= (A) -1 (B) 1 (C) 0 (D) none of these

Evaluate lim_(n->oo)1/nsum_(r=n+1)^(2n)log_e(1+r/n)

If sum_(r=0)^(n)((r+2)/(r+1)).^n C_r=(2^8-1)/6 , then n is (A) 8 (B) 4 (C) 6 (D) 5

If sum_(r=0)^(n-1)log_(2)((r+2)/(r+1)) =prod_(r=10)^(99)log_(r) (r+1), then 'n' is equal to (A) 4 (B) 3 (C) 5 (D) 6

If f(x) is integrable over [1,2], then int_1^2f(x)dx is equal to (a) ("lim")_(ntooo)1/nsum_(r=1)^nf(r/n) (b) ("lim")_(ntooo)1/nsum_(r=n+1)^(2n)f(r/n) (c) ("lim")_(ntooo)1/nsum_(r=1)^nf((r+n)/n) (d) ("lim")_(ntooo)1/nsum_(r=1)^(2n)f(r/n)

If a_(n) = sum_(r=0)^(n) (1)/(""^(n)C_(r)) , find the value of sum_(r=0)^(n) (r)/(""^(n)C_(r))

Prove the following identities: (a) (log_(a) n)/(log_(ab) n) = 1+ log_(a) b" "(b) log_(ab) x = (log_(a) x log_(b) x)/(log_(a) x + log_(b) x) .

The value of lim_(ntooo)sum_(r=1)^(n)cot^(-1)((r^(3)-r+1/r)/2) is