Question

P(k)
1^3 + 2^3 + 3^3 + ..... + k^3 = (1+2+3+...+k)^2

P(k+1)
1^3 + 2^3 + 3^3 + .... + k^3 +(k+1)^3 = (1 + 2 + 3 + .... + k(k+1))^2

Please help me to prove that it's true

Answer 1

what method of proof you wan using for this ?

Answer 2

Math induction. It's on the second step

Answer 3

i believe you already did the first step where we assume the statement is true for n=1
\[ \rm \color{Red}{1^3 + 2^3 + 3^3 + ..... + k^3} = \color{blue}{(1+2+3+...+k)^2} \]
\[\large\rm \color{Red}{1^3 + 2^3 + 3^3 + .... + k^3 }+(k+1)^3 = (1 + 2 + 3 + .... + k(k+1))^2 \]
can we replace red part with blue one right ??
\[\large\rm \color{blue}{(1+2+3+...+k)^2}+(k+1)^3 = (1 + 2 + 3 + .... + k(k+1))^2 \]

Answer 4

wait can i see the original question ?? :P

Answer 5

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

Thank u soo muchhh