- #1
ptex
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Step 0)
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Code:
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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