Prove that `1+2+3+4........+N<1/8(2n+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+2*3+3*4+.....+n*(n+1)=(n(n+1)(n+2))/(3)

Using the principle of mathematical induction, prove that 1.2+2.3+3.4+......+n(n+1)=(1)/(3)n(n+1)(n+2)

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 .

Prove that by 1.2+2.3+3.4+…..+n(n+1)=(n(n+1)(n+2))/3 by using the principle of mathematical induction for all n in N .

Using the principle of mathematical induction,prove that :.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/(1. 2. 3)+1/(2. 3. 4)+1/(3. 4. 5)++1/(n(n+1)(n+2))=(n(n+3))/(4(n+1)(n+2) for all n in N

Using the principle of mathematical induction prove that 1/(1. 2. 3)+1/(2. 3. 4)+1/(3. 4. 5)++1/(n(n+1)(n+2))=(n(n+3))/(4(n+1)(n+2) for all n in N

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