Easy: Solve T(n)=T(n-1)+n by Iteration Method

Question

Can someone please help me with this ?

Use iteration method to solve it. T(n) = T(n-1) +n

Explanation of steps

Answer 1

Expand it!

T(n) = T(n-1) + n = T(n-2) + (n-1) + n = T(n-3) + (n-2) + (n-1) + n

and so on, until

T(n) = 1 + 2 + ... + n = n(n+1)/2   [= O(n^2)]

provided that T(1) = 1