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Homework Statement
Prove that for n [tex]\geq[/tex] 1
n
[tex]\sum[/tex] m[tex]^{2}[/tex] = (1/6)*n(n+1)(2n+1)
m=1
Homework Equations
The Attempt at a Solution
Base Case:
n=1
(1)^2 = (1/6)*(6)
1=1
Inductive Step:
Assume n=k
k
[tex]\sum[/tex] m^2 = (1/6)*k(k+1)(2k+1) is true
m=1
Let n=k+1
k+1
[tex]\sum[/tex] m^2 = (1/6)*(k+1)((k+1)+1)(2(k+1)+1)
m=1
Any hints to prove this? I've tried simplifying the last equation but I haven't had any luck