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

Another solution:

T(n) = T(n-1) + n
     = T(n-2) + n-1 + n
     = T(n-3) + n-2 + n-1 + n
     // we can now generalize to k
     = T(n-k) + n-k+1 + n-k+2 + ... + n-1 + n
     // since n-k = 1 so T(1) = 1
     = 1 + 2 + ... + n    //Here 
     = n(n-1)/2
     = n^2/2 - n/2
     // we take the dominating term which is n^2*1/2 therefor 1/2 = big O
     = big O(n^2)