 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2014/discrete-mathematics-continuous-mathematics-and-probability/2/e/ii/solution

For fixed

n \geq 0

k

. At

k = 0

, both sides equal one. If the hockey-stick identity holds at

k

\sum_{i = 0}^{k + 1} (i n + i) = (k n + k + 1) + (k + 1 n + k + 1) = (k + 1 n + k + 2) .

This is the required formula with

k

replaced by

k + 1

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