If `sum _(r=1)^n (r^2+1)r! =200xx201!` Then n=` (A) 200 (B) 201 (C) 199 (D) none of these

If C_r stands for .^nC_r and sum_(r=1)^n (r.C_r)/(C_(r-1)) =210 then n= (A) 19 (B) 20 (C) 21 (D) none of these

If the coefficient of x^100 is in 1+(1+x)+(1+x)^2+(1+x)^3+………+(1+x)^n , (n >= 100) is ^201C_101 then n (A) 100 (B) 200 (C) 101 (D) none of these

Let a= 1/(n!) + sum_(r=1)^(n-1) r/((r+1)!), b= 1/(m!)+sum_(r=1)^(m-1) r/((r+1)!)then a+b= (A) 0 (B) 1 (C) 2 (D) none of these

If a=sum_(r=1)^oo(1/r)^2, b=sum_(r=1)^oo1/((2r-1)^2), then a/b= (A) 5/4 (B) 4/5 (C) 3/4 (D) none of these

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

Find sum of sum_(r=1)^n r . C (2n,r) (a) n*2^(2n-1) (b) 2^(2n-1) (c) 2^(n-1)+1 (d) None of these

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

f(1)=1 and f(n)=2sum_(r=1)^(n-1) f (r) . Then sum_(n=1)^mf(n) is equal to (A) 3^m-1 (B) 3^m (C) 3^(m-1) (D)none of these

If (+x)^n=sum_(r=0)^n a_r x^r&b_r=1+(a_r)/(a_(r-1))&prod_(r=1)^n b_r=((101)^(100))/(100!), then equals to: 99 (b) 100 (c) 101 (d) None of these

lim_(n to oo)sum_(r=1)^(n)cot^(-1)(r^(2)+3//4) is (a) 0 (b) tan^(-1)1 (c) tan^(-1)2 (d) None of these