Use mathematical induction to prove the statement is true for all positive integers n. the integer n3 + 2n is divisible by 3 for every positive integer n.

1. prove it is true for n=1
2. assume n=k
3. prove that n=k+1 is true as well

so

1.
=
=
=1
we got a whole number, true

2.

if everything clears, then it is divisble

3.
=
=
=

we know that if z is divisble by 3, then z+3 is divisble b 3
also, 3k/3=a whole number when k= a whole number

=
=
since the k²+k+1 part cleared, it is divisble by 3

we found that it simplified back to

done

Multiplication property of zero