Recurrence Relation: Finding Big O

Question

Hello,

I'm trying to find Big O of this recurrence relation:

T(n) = T(n-1) + n^c // where c is >=1

So I decided to solve this by using a recursion tree, which I have broken down as follows:

n^c -> (n-1)^c -> (n-2)^c -> ... -> (n-i)^c

I then formed the following sum:

from 0 to n-1:
   (n-i)^c

Reducing this sum gives: (n-(n-1))^c = (1)^c

So then would the correct Big O notation be O(n)? Thanks.