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

The value of 1+1.1!+2.2!+3.3!+.........+n.n! is (A) (n+1)!+1(B)(n-1)!+i(C)(n+1)!-1(D)(n+1)!

the value of 1.1!+ 2.2!+ 3.3!+ ....+ n.n!

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

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

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

Prove by the principle of mathematical induction, that 1.1!+2.2!+3.3!+.....+(n.n!)=(n+1)!-1"for all natural number "n (n!=1xx2xx3....n)

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).......3n) / n^(2n))^(1/n)is equal to