Recurrence Relation: Finding Big O
问题 I am trying to find the big O bound for the following recurrence relation: T(n) = T(n-1) + n^c, where c >= 1 is a constant So I've decided to solve this by using iteration: T(n) = T(n-1) + n^c T(n-1) = T(n-2) + (n-1)^c T(n) = T(n-2) + n^c + (n-1)^c T(n-2) = T(n-3) + (n-2)^c T(n) = T(n-3) + n^c + (n-1)^c + (n-2)^c T(n) = T(n-k) + n^c + (n-1)^c + .... + (n-k+1)^c Suppose k = n-1, then: T(n) = T(1) + n^c + (n-1)^c + (n-n+1+1)^c T(n) = n^c + (n-1)^c + 2^c + 1 I'm not sure if this is correct