`1+3+6+10+...+((n-1)n)/2+((n+1)n)/2=`

lim_ (n rarr oo) (1) / (n ^ (3)) {1 + 3 + 6 + ...... + (n (n + 1)) / (2)}

If S_(n)=1+3+6+10+...+(n(n+1))/(2) then S_(n) is

If S_(n)=1+3+6+10+...+(n(n+1))/(2) then S_(n) is

(1)/(n-1)-(10)/(n+2)=3

If ninNN , then by princuple of mathematical induction prove that, n*1+(n-1)*2+(n-2)*3+ . . . +2*(n-1)+1*n=(1)/(6)n(n+1)(n+2)

lim_ (n rarr oo) (1 + 3 + 6 ++ (1) / (2) n (n + 1)) / (n ^ (3))

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) + ….

lim_ (n rarr oo) ((1) / (n + 1) + (1) / (n + 2) + (1) / (n + 3) + ...... + (1) / (6n ))

lim_(n rarr oo) 1/n^(3) { 1+3+6+...+ (n(n+1))/2} =