Mathemtical Induction Proof (Stuck on induction)

$Prove 1^k+2^k+...+n^k <= n^(k+1), k is a real number greater than 0 and n is an integer greater than 0.$

1. P(n): $1^k+2^k+... n^k <= n^k+1$
2. $P(1) 1^k +2^k +... +1^k <= 1^k+1<br /> 1^k<=1^k+1, true$
3. Assume: P(n): $1^k+2^k+... = n^k <= n^k+1$
4. Prove(n+1)
$n^k+1 + n^k <= n^k+1<br /> n^k+1+(n+1)^k <= (n+1)^k+1$

// Im stuck on how to manipulate this part of the equation, i guess i need to refresh in algebra. Am in correct up till this point, and any suggestions on how to finish this? Thanks and gretaly appreciated.