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

1^(2) + 1+ 2^(2) + 2 + 3^(2) + 3+"............"+n^(2) + n is equal to :

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

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

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

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

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