If \( (2.1+1)+(2.2+1)+\ldots+(2 n+1)=n^{2}+2 n+11, n \in \mathbf{N}...

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If \( (2.1+1)+(2.2+1)+\ldots+(2 n+1)=n^{2}+2 n+11, n \in \mathbf{N} \) is true for \( n=m \), then prove that it is also true for \( n=m+1 \). Can we conclude that it is true for all \( n \in \mathbf{N} \) ?
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