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2[sup]2[/sup] + 4[sup]2[/sup] + 6[sup]2[/sup]+...+(2n)[sup]2[/sup] = 2n(n+1)(2n+1)/3

Step 1)

Let n = 2

2[sup]2[/sup] + 4[sup]2[/sup]

= 4 + 16

= 20

2(2)(2+1)(2(2)+1)/3

= 60/3

= 20

Step2)

Assume that the formula works for n=1,2,3,...,k

ie. 2[sup]2[/sup] + 4[sup]2[/sup] + 6[sup]2[/sup]+...+(2n)[sup]2[/sup] = 2k(k+1)(2k+1)/3

Step 3)

2n(n+1)(2n+1)/3 + (k+1)[sup]2[/sup]

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# Homework Help: Am I on the right track with this induction question?

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