" 1."1+2+3+...+n=(1)/(2)n(n+1)

1.2+2.3+3.4+.........+n(n+1)=(1)/(3)n(n+1)(n+3)

A) |lim_(n rarr oo)((n^((1)/(2)))/(n^((3)/(2)))+(n^((1)/(2)))/((n+3)^((3)/(2)))+....+(n^((1)/(2)))/( n+3(n-1) ^((3)/(2))))=

1.2.3+2.3.4+....+n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/4

Prove by mathematical induction 1/1.2 + 1/2.3 + . . .+ 1/((n)(n+1)) =n/((n+1))

1/1.2 + 1/2.3 +…..+ 1/(n(n+1)) = n/(n+1)

If P(n) :1+4+7…….+(3n-2)=(1)/(2)n(3n-1) .Verify P(n) for n =1,2.

Prove that ((2n+1)!)/(n !)=2^n{1. 3. 5 .........(2n-1)(2n+1)}

Find the sum of the series: 1. n+2.(n-1)+3.(n-2)++(n-1). 2+n .1.

Find the sum of the series: 1. n+2.(n-1)+3.(n-2)++(n-1). 2+n .1.

1.2.3+2.3.4++n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/(4)