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

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

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

If a_(1), a_(2), a_(3), ……. , a_(n) are in A.P. and a_(1) = 0 , then the value of (a_(3)/a_(2) + a_(4)/a_(3) + .... + a_(n)/a_(n - 1)) - a_(2)(1/a_(2) + 1/a_(3) + .... + 1/a_(n - 2)) is equal to

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

The value of (6^(n+3) - 32.6^(n+1))/(6^(n+2) - 2.6^(n+1)) is equal to