If n is 1, then `n (n^2 - 1)` is

If alpha in R, n in N " and " n + 2 (n - 1)+ 3 (n-2) + …… +(n-1)2 + n.1 = alpha n ( n + 1) (n + 2) , " then " alpha =

Sum of the series S_(n) =(n) (n) + (n-1) (n+1) + (n-2) (n+2) + …+ 1(2n-1) is

Evalute lim_ (n rarr oo) [(1) / ((n + 1) (n + 2)) + (1) / ((n + 2) (n + 4)) + ...... + ( 1) / (6n ^ (2))]

let =(1)/(n*(n+1))+(1)/((n+1)*(n+2))+(1)/((n+2)(n+3))+... terms then lim_(n rarr oo)S_(n) is equal to