`(n+2)nC_0(2^(n+1))-(n+1)nC_1(2^(n))+(n)nC_2(2^(n-1))-....` is equal to

The value of .^(n)C_(0) xx .^(2n)C_(r) - .^(n)C_(1)xx.^(2n-2)C_(r)+.^(n)C_(2)xx.^(2n-4)C_(r)+"…." is equal to

lim_(nrarroo) [(1)/(n)+(n^(2))/((n+1)^(3))+(n^(2))/((n+2)^(3))+...+(1)/(8n)] is equal to

If n = 5, then (""^(n)C_(0))^(2)+(""^(n)C_(1))^(2)+(""^(n)C_(2))^(2)+......+(""^(n)C_(5))^(2) is equal to

The value of ("^n C_0)/n + ("^nC_1)/(n+1) + ("^nC_2)/(n+2) +....+ ("^nC_ n)/(2n) is equal to

If "^(n)C_(0)-^(n)C_(1)+^(n)C_(2)-^(n)C_(3)+...+(-1)^(r )*^(n)C_(r )=28 , then n is equal to ……

If |x|<1,t h e n1+n((2x)/(1+x))+(n(n+1))/(2!)((2x)/(1+x))^2+...... is equal to

lim_(n -> oo) (((n+1)(n+2)(n+3).......3n) / n^(2n))^(1/n) is equal to

If (1+x)^n=C_0+C_1x+C2x2++C_n x^n , n in N ,t h e nC_0-C_1+C_2-+(-1)^(n-1)C_(m-1), is equal to (mltn)

lim_(n rarr 0)(1/(1+n^(2))+2/(1+n^(2))+3/(1+n^(2))+....+n/(1+n^(2))) is equal to

The value of sum sum_(n=1)^(oo)cot^(-1)(((n^(2)+2n)(n^(2)+2n+1)+1)/(2n+2)) is equal to