# Math Help - Mathematical Induction proving

1. ## Mathematical Induction proving

$n^{3}+2n$

prove that it is divisible by 3 for any integer $n\geq 1$
the steps i use are
1) plug in a number to see if its true 1+2 = 3 is divisible by 3= true
2). K=N plug it in $k^{3}+2k$
3) K+1 =N plug it in $k^{3}+2k+ (k+1)^{3} +2(k+1)$ ---- this is where I'm confused i usually have numbers for example 1+3+4+5+.......(3n+2) = n(n+1)
I'm not sure if step 3 is right because that's what i do for my usual example with numbers

2. ## Re: Mathematical Induction proving

Hint: add $(n+1)^3+2(n+1)-(n^3+2n)=3(n^2+n+1)$ to your induction hypothesis.

3. ## Re: Mathematical Induction proving

Same thing:
$(n+1)^3+ 2(n+1)= n^3+ 3n^2+ 3n+ 1+ 2n+ 2= (n^3+ 2n)+ (3n^2+ 3n+ 3)= (n^3+2n)+ 3(n^2+ n+ 1)$.