Question

Prove that n^2 + 5n is divisible by 2 where n is in N.

Answer 1

\[n^{2}+5n\] is divisible by 2 where \[n \in N\]

Answer 2

hint : mathematical induction

Answer 3

Yeah I know mathematical induction, but that does not help.

Answer 4

well it does.
we first check for n=1 for example
and see that it works since 6/2 = 3.
now we assume that it works for n=k
so that k^2+5k is divisible by 2

now we check what happens with k+1 :
(k+1)^2 + 5(k+1)
is it divisible by 2 (assuming k^2+5k is) ?

Answer 5

and use the fact that even + even = even :)

Answer 6

Multiply some and see if you can use what coolsector and hartnn said. Like look for k^2+5k. Look to use what you assumed before doing the induction step.