Induction on sum of natural numbers

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Reference no: EM13121872

Let f:N x N -> N be the function defined recursively as follows:

f(0, 0) = 6

f(i, j) = f(i - 1, j) + 2 if i > 0 and j = 0

f(i, j) = f(i, j - 1) + 1 if j > 0

Use induction on the sum i + j to prove that f(i, j) = 2i + j + 6 for all (i, j) in N x N.

Reference no: EM13121872

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