दिखाइए कि ` n ! (n +2) = n ! + (n + 1)! `

lim_ (n rarr oo) n ^ (- n ^ (2)) ((n + 1) (n + (1) / (2)) (n + (1) / (2 ^ (2))) .... (n + (1) / (2 ^ (n-1)))) ^ (n)

lim_ (n rarr oo) ((n) / (n ^ (2) +1) + (n) / (n ^ (2) +2) + (n) / (n ^ (2) +3) +. .. (n) / (n ^ (2) + n))

If n is a non zero rational number then show that 1 + n/2 + (n (n - 1))/(2.4) + (n(n-1)(n - 2))/(2.4.6) + ….. = 1 + n/3 + (n (n + 1))/(3.6) + (n (n + 1) (n + 2))/(3.6.9) + ….

If n is a non zero rational number then show that 1 + n/2 + (n (n - 1))/(2.4) + (n(n-1)(n - 2))/(2.4.6) + ….. = 1 + n/3 + (n (n + 1))/(3.6) + (n (n + 1) (n + 2))/(3.6.9) + ….

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 =

lim_ (n rarr oo) (1) / (n) [(1) / (n + 1) + (2) / (n + 2) + ... + (3n) / (4n)]

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