SOLUTION: How can I prove that for each positive integer n, the sum of the first n odd positive integers is n^2 using induction?

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Question 856463: How can I prove that for each positive integer n, the sum of the first n odd positive integers is n^2 using induction?
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
step1 check P%5B1%5D
S%5B1%5D=1%5E2=1 (so true for first case)
step2 check that P%5Bk%5D implies P%5Bk%2B1%5D
in this case...
S%5Bn%5D+%2B+a%5Bn%2B1%5D+=+S%5Bn%2B1%5D
n%5E2%2B2n%2B1=%28n%2B1%29
true so we are done (it must be true for all n)