Prove by mathematical induction `1+2+3+……+n(n(n+1))/(2)`.

Prove by mathematical induction that 1^3+2^3+……+n^3=[(n(n+1))/2]^2

Prove by mathematical induction that sum_(r=0)^(n)r^(n)C_(r)=n.2^(n-1), forall n in N .

Prove the following by the principle of mathematical induction: 1^2+2^2+3^2++n^2=(n(n+1)(2n+1))/6

Prove the following by the principle of mathematical induction: \ 1. 3+2. 4+3. 5++(2n-1)(2n+1)=(n(4n^2+6n-1))/3

Prove by the mathematical induction x^(2n)-y^(2n) is divisible by x+y

Prove that by using the principle of mathematical induction for all n in N : (1)/(2.5)+ (1)/(5.8) + (1)/(8.11)+ ...+(1)/((3n-1)(3n+2))= (n)/(6n+4)

Prove by mathematical induction that 10^(2n-1)+1 is divisible by 11

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

Prove that by using the principle of mathematical induction for all n in N : (1)/(2)+ (1)/(4)+ (1)/(8)+ ......+ (1)/(2^(n))= 1-(1)/(2^(n))

Let u_(1)=1,u_2=2,u_(3)=(7)/(2)and u_(n+3)=3u_(n+2)-((3)/(2))u_(n+1)-u_(n) . Use the principle of mathematical induction to show that u_(n)=(1)/(3)[2^(n)+((1+sqrt(3))/(2))^n+((1-sqrt(3))/(2))^n]forall n ge 1 .