If `sum_(r=0)^(203)((r^(2)+2)(r+1)!+2r(r+1)!)=a!-2(b)` (where `a,b in N`), then `a-b` is equal to_____

If sum_(r=1)^(oo)((2r-1))/((r^(2)+1)(r^(2)-2r+2))=(a)/(b) (where a & b are co-prime, n>=2 ), then a and b will be

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 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)^(10).^(10)C_(r)(2)^(20-r)(3)^(r-1)=(a^(10)-b^(10))/(3) then (a-b) is equal to

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

sum_(r=0)^n((-1)^r*C_r)/((r+1)(r+2)(r+3))=1/(a(n+b)), then a+b is

If sum_(r=1)^(n)r(r+1)+sum_(r=1)^(n)(r+1)(r+2)=(n(an^(2)+bn+c))/(3),(a,b,cinN) then

sum_(r=1)^(n)(C(n,r))/(r+2) is equal to

sum_(r=0)^(n)r(r+1)(r+2)(r+3) is equal to