SOLUTION: Prove that
1^2 + 3^2 + . . . + (2n − 1)^2 =1/3(4n^3 − n)
for all natural numbers n.
Algebra.Com
Question 1023504: Prove that
1^2 + 3^2 + . . . + (2n − 1)^2 =1/3(4n^3 − n)
for all natural numbers n.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
+ . . . +
Proof by induction.
For n = 1, the statement is trivially true.
Assume the statement is true for some natural number n = k,
or
+ . . . +
Then by adding on both sides, we get
+ . . . +
=, and the statement is proved...
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