I'm new to Proof by Induction. I've gotten a few so far, but this one has eluded me for some reason.(adsbygoogle = window.adsbygoogle || []).push({});

" Prove that [tex] 1^3 + 2^3 + 3^3.....k^3 = (1 +2 + 3....k)^2 [/tex]"

I checked for n =1 and , yes it does work. So, I assumed A(k) is true, so I'll try for A(k+1)

I started assuming A(k) and added [tex] (k+1)^3 [/tex] to both sides (as this would be the next term

[tex] 1^3 + 2^3 .... k^3 + (k+1)^3 = (1 + 2.... k)^2 + (k+1)^3 = (1 + 2....k + (k + 1) )^2 [/tex]

So, I must now show that

[tex](1 +2 + .... k + (k+1))^2 = (1 + 2 + ....k)^2 + (k+1)^3 [/tex]

Does this look right so far?

Unfortunately, I haven't thought of a way to demonstrate this yet. If I prove that statement true, I prove the original assertion. Should I try proving that statement with induction or something...?

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# Proof by Induction question

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