Solving a recurrence relation using iteration method

Question

how to solve T(n) = T(n-1) + n using Iterative method and answer is theta(n^2)

Answer 1

T(n) = T(n-1) + n = T(n-2) + n-1 + n = ... = 1+ 2 + ... + n = (n+1)n/2 = theta(n^2)

note the assumption that T(0) = 0 (you must have base for the recursion)
hope that what you have meant

Answer 2

At times, you could also use characteristics equations method to solve recurrence relations. This involves determining Particular integral and total solution.

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