Friday, April 19, 2019

algebra precalculus - I'm having trouble with induction. Prove 1+23+33+...+n3=frac((n2)(n+1)2)4





I started a new course and I'm expected to know this stuff, and I'm having trouble learning some on my own.
I'm stuck with this problem:
Prove 1+23+33+...+n3=((n2)(n+1)2)4 using induction (the 1+23... is written in sum notation, although I don't know how to enter that here, sorry).
I started substituting nn+1 but I don't know what to do next. Any help would be extremely appreciated.


Answer



1+23+...+n3+(n+1)3=Hyp.n2(n+1)24+(n+1)3=n2(n+1)2+4(n+1)34=(n+1)2(n2+4n+4)4=(n+1)2(n+2)24.


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