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PrecalculusChallengeSequences, Series, and the Binomial Theorem

Sequences, Series, and the Binomial Theorem · Challenge problem

Using the standard closed forms for ∑k2\sum k^2, ∑k\sum k, and ∑1\sum 1, simplify ∑k=1n(2k−1)2\displaystyle\sum_{k=1}^{n}(2k-1)^2 to a single factored expression in nn.