Using induction to prove something

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Mahonroy

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Hello,
Came across this problem, and I was confused as to how to go about proving this. Any help is greatly appreciated, thanks!
 

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1) Prove that it starts.
2) Prove that one implies the next.

Let's see what you get.
 
There is a process that involves P(n), P(k), and P(K+1). From reading it looks like the P(K+1) is supposed to be equal to P(k) which shows that its true but it didn't look like they were equal.
 
Mahonroy said:
There is a process that involves P(n), P(k), and P(K+1). From reading it looks like the P(K+1) is supposed to be equal to P(k) which shows that its true but it didn't look like they were equal.
Click to expand...
\(\displaystyle P(1)=3\)
\(\displaystyle P(K)=K^3+2K\)
\(\displaystyle P(K+1)=K^3+3K^2+1+2K+2=(K^3+2K)+3(K^2+K+1)\)
 
Thanks again for the reply!
I don't understand how you are substituting in the k+1 into the equation, and how you end up with the final equation. How does this prove this? Thanks again for the help.
 
Mahonroy said:
Thanks again for the reply!
I don't understand how you are substituting in the k+1 into the equation, and how you end up with the final equation. How does this prove this? Thanks again for the help.
Click to expand...
Don't just stare at the solution - use pencil/paper and fill out the missing steps. I'll do one missing step for you.

P(K+1) = (K + 1)[sup:yd8t9fgy]3[/sup:yd8t9fgy] + 2* (K +1)
 
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