(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

1b) Prove by induction: [itex]1^{3}+...+n^{3}=(1+...+n)^{2}[/itex]

2a) Find a formula for: [itex]\sum^{n}_{i=1}(2i-1)[/itex]

2. Relevant equations

There's a Hint for 2a): 'What to this expression have to do with [itex]1+2+3+...+2n[/itex]?'

3. The attempt at a solution

In 2a) I've got near the answer, when comparing with the given one, but I can't understand the last thing he does. The solution in the book is:

[itex]\sum^{n}_{i=1}(2i-1)=1+2+3+...+2n-2(1+...+n)

=(2n)(2n+1)/2-n(n+1)[/itex]

And I couldn't understand how to make the second member become the third one, which goes directly to the answer [itex]n^{2}[/itex]

Thanks

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# Homework Help: Spivak 2-1b, 2-2a (induction)

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