Using the principle of mathematical induction prove that for all \(...

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Using the principle of mathematical induction prove that for all \( n \in N \) :
\[
1.3+3.5+5.7+\ldots \text { to } n \text { terms }=\frac{1}{3} n\left(4 n^{2}+6 n-1\right) .
\]
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