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 a=sum_(r=1)^oo 1/r^4 then sum_(r=1)^oo 1/((2r-1)^4)=

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)^(oo) 1/((2r-1)^(2)), then (3a)/b is equal to _____

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

sum_(r=1)^10 r/(1-3r^2+r^4)

Let S_n=sum_(r=0)^oo 1/n^r and sum_(n=1)^k (n-1)S_n = 5050 then k= (A) 50 (B) 505 (C) 100 (D) 55

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

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 sum_(r=1)^(oo) (C^r)/(r!) =1 then C =

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