S=1^(3)+2^(3)+3^(3)+cdots+n^(3)=[(n(n+1))/(2)]^(2)

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

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

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

lim_(n rarr oo)(n(1^(3)+2^(3)+3^(3)+cdots n^(3))^(2))/((1^(2)+2^(2)+3^(2)+cdots+n^(2))^(3)) =

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))/(4), n in N

S_(n) = 1^(3) + 2^(3) + 3^(3) + …... + n^(3) and T_(n) = 1+ 2 + 3+ 4…...n

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

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