Solved: Use generalized induction as was done in Example

Chapter 5, Problem 46E

(choose chapter or problem)

Use generalized induction as was done in Example 13 to show that if \(a_{m, n}\) is defined recursively by \(a_{1,1}=5\) and

\(a_{m, n}= \begin{cases}a_{m-1, n}+2 & \text { if } n=1 \text { and } m>1 \\ a_{m, n-1}+2 & \text { if } n>1,\end{cases}\)

then \(a_{m, n}=2(m+n)+1\) for all \((m, n) \in \mathbf{Z}^{+} \times \mathbf{Z}^{+}\).

Equation Transcription:

Text Transcription:

a_{m, n}

a_{1,1}=5

a_{m, n}= a_{m-1, n}+2 &  { if } n=1 \text { and } m>1 \\ a_{m, n-1}+2 &  { if } n>1,

a_{m, n}=2(m+n)+1

(m, n) \in Z^{+} X Z^{+}