Use a proof by induction to prove that for all n EN, 1+3+5+...+(2n-1)= 1 (2j-1) = n². 9. (9 n², that is, that

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Use a proof by induction to prove that for all \( n \in \mathbb{N} \), \( 1 + 3 + 5 + \ldots + (2n - 1) = n^2 \), that is, that \( \sum_{j=1}^{n} (2j - 1) = n^2 \).
Transcribed Image Text:Use a proof by induction to prove that for all \( n \in \mathbb{N} \), \( 1 + 3 + 5 + \ldots + (2n - 1) = n^2 \), that is, that \( \sum_{j=1}^{n} (2j - 1) = n^2 \).
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