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_(t=1)^(1003) (r^(2) + 1)r! = a! - b(c!) where a, b, c in N the least value of (a + b + c) is pqrs then

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=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 sum_(r=1)^(n) r(r+1) = ((n+a)(n+b)(n+c))/(3) , where a gt b gt c , then

If sum_(r=1)^(r=n)(r^(4)+r^(2)+1)/(r^(4)+r)=(675)/(26) , then n equal to

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 (A) a + b + c = 24 (B) 2a + b - c = 0 (C) a - b + c= 6 (D) ab + bc + ca = 11

sum_(r=1)^n (a^r +br) , a , b in R^+ is equal to :

The value of sum_(r=1)^(n+1)(sum_(k=1)^n "^k C_(r-1)) ( where r ,k ,n in N) is equal to a. 2^(n+1)-2 b. 2^(n+1)-1 c. 2^(n+1) d. none of these

If sum_(r=1)^(oo)(1)/((2r-1)^(2))=(pi^(2))/(8) , then sum_(r=1)^(oo) (1)/(r^(2)) is equal to

sum_(r=1)^n (r^2 - r-1)/((r+1)!) is equal to :