`1+1.1!+2.2!+3.3!+......+n*n!` is equal to

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

Value of 1+1/(1+2)+1/(1+2+3)+....+1/(1+2+3+....+n) is equal to

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

Using mathematical induction, to prove that 1*1!+2*2!+3.3!+ . . . .+n*n! =(n+1)!-1 , for all n in N

If ,Z_1,Z_2,Z_3,........Z_(n-1) are n^(th) roots of unity then the value of 1/(3-Z_1)+1/(3-Z_2)+..........+1/(3-Z_(n-1)) is equal to

lim_(n->oo) {1/1.3+1/3.5+1/5.7+.....+1/((2n+1)(2n+3)) is equal to

If (1+x)^n=a_0+a_1x+a_2x^2+....+a_nx^n , then (a_0-a_2+.....)^2+(a_1-a_3+.....)^2 is equal to (A) 3^n (B) 2^n (C) ((1-2^n)/(1+2^n)) (D) none of these

lim_(n rarr oo)((n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2)) + (n)/(n^(2)+3^(2))+......+(1)/(5n)) is equal to :

The sum 1 + 3 + 3^(2) + …+ 3^(n) is equal to

If a 1 , a 2 , a 3 , , a 2 n + 1 are in A.P., then a 2 n + 1 − a 1 a 2 n + 1 + a 1 + a 2 n − a 2 a 2 n + a 2 + + a n + 2 − a n a n + 2 + a n is equal to a. n ( n + 1 ) 2 × a 2 − a 1 a n + 1 b. n ( n + 1 ) 2 c. ( n + 1 ) ( a 2 − a 1 ) d. none of these