Solve the recurrence equation T(n) = T(n−1) + n T(1) = 1

Given recurrence relation: T(n) = T(n−1) + n with base case T(1) = 1

Step 1: Expand the recurrence

T(n) = T(n−1) + n T(n) = [T(n−2) + (n−1)] + n T(n) = T(n−3) + (n−2) + (n−1) + n ...

Step 2: Continue until base case

T(n) = T(1) + 2 + 3 + ... + (n−1) + n T(n) = 1 + 2 + 3 + ... + (n−1) + n

Step 3: Apply arithmetic series formula

Sum of first n natural numbers: S = n(n+1)/2 Therefore, T(n) = n(n+1)/2

Final Answer: n(n+1)/2