SOLUTION: use mathematical induction to prove that 1^2 + 2^2 + 3^2 +...+ n^2 = n(n+1)(2n+1)/6 for all positive integral values of n

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Question 229820: use mathematical induction to prove that
1^2 + 2^2 + 3^2 +...+ n^2 = n(n+1)(2n+1)/6
for all positive integral values of n
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




prove



1. Show that



is true for





and



2. Assume



is true for

some positive integer , then show

the relationship is true for , namely that:



First note that:



which can be written:



because we assumed the relationship to be true for some positive integer .

But



(Verification of the previous step is left as an exercise for the student)

And



(Verification of the previous step is also left as an exercise for the student)

Therefore, if the statement is true for some , it must be true for . Since it was proven true for , it must be true for , then it must be true for ...

John