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. 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?