`1^(3)+2^(3)+3^(3)+.....+n^(3)=(n(n+1)^(2))/(4), n in N`

1^(3)+2^(3)+3^(3)+...+n^(3)=n^(2)((n+1)^(2))/(4)

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

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

Prove by PMI that 1.2+2.3+3.4+....+n(n+1)=((n)(n+1)(n+2))/(3),AA n in N

(1)/(1.2)+(1)/(2.3)+(1)/(3.4)+.......+(1)/(n(n+1))=(n)/(n+1),n in N is true for

Prove the following by using the principle of mathematical induction for all n in Nvdots1.3+2.3^(2)+3.3^(3)+...+n.3^(n)=((2n-1)3^(n+1)+3)/(4)

1.3+2.3^(2)+3.3^(3)+............+n.3^(n)=((2n-1)3^(n+1)+3 )/(4)

Using the principle of mathematical induction prove that : the 1.3+2.3^(2)+3.3^(3)++n.3^(n)=((2n-1)3^(n+1)+3)/(4) for all n in N.

(1^(3)+2^(3)+...+n^(3))/(1+3+5+...+(2n-1))=((n+1)^( 2))/(4)