Hi all, been struggling with my course material regarding Induction. My prof is really not great at explaining this proof method. I don't know what the learning curve or expectations here are like but I'm really struggling with this conceptually.(adsbygoogle = window.adsbygoogle || []).push({});

Any assistance with these problems would be much appreciated:

1. Prove that 3 divides n^3+2n whenever n is a positive integer.

I know I can't use a summation progression so how do I solve this induction?

(n+1)^3+2(n+1) is the next step but I get lost when I try to factor out the (n+1)^3

This is as far as I can take this one.

2. Prove that 1x1! + 2x2! + ... + nxn! = (n+1)!-1

Let P(n) be 1x1!+…+nxn!=(n+1)!-1

Basis Step: 1 x 1! = (1+1)!+1

1 = 1

Therefore our basis step is true.

Inductive Step: We know that P(n) is true thus we must prove P(n+1)

1x1!+…+nxn!+((n+1)(n+1)!)=[ 1x1!+…+nxn! ] + ((n+1)(n+1)!)

1x1!+…+nxn!+((n+1)(n+1)!)= [(n+1)!-1]+((n+1)(n+1)!)

1x1!+…+nxn!+((n+1)(n+1)!)= ((n+1)(n+1)!)

I believe this one is solved however I'm not sure if I must take it further?

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# Induction Question

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