- #1
Fizex
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I'm trying to solve this problem from CH2 of spivak's calculus of which I am self-studying.
Prove the following by mathematical induction:
[tex]1^3+...+n^3=(1+...+n)^2[/tex]
To prove by mathematical induction, you test whether P(1) is true and if P(k) is true then P(k+1) is true.
[tex]1^3+...+n^3=(1+...+n)^2[/tex]
[tex]1^3+...+n^3+(n+1)^3=(1+...+n)^2+(n+1)^3[/tex]
[tex](1+...+n)^2+(n+1)^3=(1+...+n+1)^2[/tex]
From there I have no clue and I've been staring at that for 15 minutes.
Homework Statement
Prove the following by mathematical induction:
[tex]1^3+...+n^3=(1+...+n)^2[/tex]
Homework Equations
To prove by mathematical induction, you test whether P(1) is true and if P(k) is true then P(k+1) is true.
The Attempt at a Solution
[tex]1^3+...+n^3=(1+...+n)^2[/tex]
[tex]1^3+...+n^3+(n+1)^3=(1+...+n)^2+(n+1)^3[/tex]
[tex](1+...+n)^2+(n+1)^3=(1+...+n+1)^2[/tex]
From there I have no clue and I've been staring at that for 15 minutes.