Question

I need some help with Induction. I was able to do the first part of proving them equal but after that...

Answer 1

\[\sum_{K=1}^{n}=1^3+2^3+3^3...+n^3=(\frac{ n(n+1) }{ 2 })^2\]

Answer 2

For Step 1 I got:
Left side= \[1^3=1\]

Right side= \[(\frac{ 1(1+1) }{ 2 })^2=1\]

Answer 3

And every time I tried to work out the rest of the problem I didn't get anything like I was suppose too...

Answer 4

you assume true for n, and show it is true for (n+1)
the sum up to n^3 is ( n (n+1)/2)^2
now add (n+1)^3

Answer 5

you have to show that this simplifies to ( (n+1)(n+2)/2 )^2

Answer 6

Try putting (n+1)^3 over the common denominator of 4:
\[ \frac{ (n (n+1))^2}{4}+\frac{4(n+1)^3}{4} \]
or
\[ \frac{ n^2 (n+1)^2+4(n+1)^3}{4} \]

Answer 7

factor out (n+1)^2 and see what you get