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^{+}
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