Prove that `1+2+3+.....n=(n(n+1))/(2)`

Prove that 1+2+3+.....+=(2n+1))=n^(2)

By the principle of mathematical induction prove that 1+2+3+4+…n= (n(n+1))/2

Prove that 1*2+2*3+3*4+.....+n*(n+1)=(n(n+1)(n+2))/(3)

Prove that 1^1*2^2*3^3....n^nle((2n+1)/3)^((n(n+1))/2) .

For all nge1 , prove that 1.2.3+2.3.4+......+n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/4

Prove that: 1+2+3+n<((2n+1)^(2))/(8) for all n in N.

Prove that : 1^2+2^2+3^2++n^2=(n(n+1)(2n+1))/6

Prove that (1)/(n+1)=(nC_(1))/(2)-(2(^(n)C_(2)))/(3)+(3(^(n)C_(3)))/(4)-...+(-1)^(n+1)(n(^(n)C_(n)))/(n+1)

Using the principle of mathematical induction, prove that : 1. 2. 3+2. 3. 4++n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/4^ for all n in N .

Using the principle of mathematical induction, prove that : 1. 2. 3+2. 3. 4++n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/4^ for all n in N .