SOLUTION: use mathematical induction to prove that {{{(1^2)+(2^2)+(3^2)}}}+...+{{{(2^n)=n^(k+1) -2}}}

Question 860335: use mathematical induction to prove that +...+
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
You want to prove that

or, using fancier symbols, that
.
You need to prove that
a) it is true for , and
b) if it is true for , then it will be true for .

For the "sum" has only one term:

and it is indeed equal to

If the formula is true for ,
.
Adding one more term, we find
,
which shows that the formula is true for .
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