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))/(4), n in N

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

Use mathematical induction to prove that statement 1^(3) + 2^(3) + 3^(3) + . . . + n^(3) = (n^(2) (n + 1)^(2))/( 4) , AA n in N

Match the following . {:(,"ColumnI",,"ColumnII"),((i) ,1^(2) +2^(2) +3^(2) +....+n^(2) ,(a) ,[(n(n+1))/(2)]^(2)),((ii) , 1^(3) +2^(3) +3^(3) +...+n^(3) ,(b), n(n+1)),((iii),2+4+6+...+2n,( c),(n(n+1)(2n+1))/(6)),((iv),1+2+3+...+n,(d),(n(n+1))/(2)):}

1^(3)+2^(3)+3^(3)+………….+n^(3)=(n^(2)(n+1)^(2))/4 forall n in N.

By the principle of mathematical induction prove that for all natural number 'n' the following statement are true : (a) 2+4+6+........ +2n =n (n+1) (b) 1+4+7+.......+(3n-2) =1/2 n (3n-1) (C) 1^(3)+2^(3)+3^(3) +..........+n^(3)=1/4 n^(2)(n+1)^(2)

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)

underset(n to oo)lim (n(1^(3)+2^(3)+...+n^(3))^(2))/((1^(2)+2^(2)+...+n^(2))^(3))=

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

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 .