`1^(3) + 2^(3) + 3^(3) + ……….. + n^(3) = ………`

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

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

If P(n):1^(3)+2^(3)+3^(3)+....+(n+1)^(3)=k ,then L.H.S.of P(2)=

If t=(1^(2)+2^(2)+3^(2)+...r^(2))/(1^(3)+2^(3)+3^(3)+....+r^(3)), S_(n) = overset(n) underset(r=1) sum(-1)^(r)t_(r) then lim_(n to oo) ((1)/(3)-S_(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)

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)

If t_(r)=(1^(2)+2^(2)+3^(2)+….+r^(2))/(1^(3)+2^(3)+3^(3)+…+r^(3)), S_(n)=sum_(r=1)^(n)(-1)^(r)t_(r) , then lim_(nrarroo)((1)/(3-S_(n)))=