Wednesday, February 10, 2016

sequences and series - Mathematical Induction: Sum of first n even perfect squares

So the series is $$P_k: 2^2 + 4^2 + 6^2 + ... + (2k)^2 = \frac{2k(k+1)(2k+1)}3$$



and i have to replace $P_k$ with $P_{k+1}$ to prove the series.



I have to show that $$\frac{2k(k+1)(2k+1)}3 + [2(k+1)]^2 = \frac{2(k+1)(k+2)(2k+3)}3$$ but I don't know how.

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