Hey, i have a question here that reads:
Prove by mathematical induction that 1³ + 1² + ... + n³ = (n²(n+1)²)/4 for any natural number n.
Could anyone get me started on this? Any help would be greatly appreciated. Thanks.
Printable View
Hey, i have a question here that reads:
Prove by mathematical induction that 1³ + 1² + ... + n³ = (n²(n+1)²)/4 for any natural number n.
Could anyone get me started on this? Any help would be greatly appreciated. Thanks.
Quote:
Originally Posted by GreenDay14
Don't you mean $\displaystyle 1^3+2^3+3^3+...+n^3$
Nope, reading it straight out of the book.
the expression $\displaystyle 1^3+1^2+...n^3$ doesnt make any sense
I will assume the book/you actually want to prove $\displaystyle \sum_{k=1}^n k^3=\frac{n^2(n+1)^2}{4}$ which is true, can you prove this now that I have stated the actual problem or do you still need help
You can look at a similar thread here.
Could you verify the first three steps? For n = 1, n = 2, and n = 3.
I think there might be a typo because in this problem you can't prove the base case for your proposition:
$\displaystyle P(1) = \frac{1^2(n+1)^2}{4} = 1 \neq (1^3 + 1^2 + 1) = 3$
If we can't prove the base case, we can't move onto the inductive step.
