document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #516469 by tommyt3rd(5050) $\"\"$ $\"About$

You can put this solution on YOUR website!
step1 check $\"P%5B1%5D\"$
\n" ); document.write( " $\"S%5B1%5D=1%5E2=1\"$ (so true for first case)\r
\n" ); document.write( "\n" ); document.write( "step2 check that $\"P%5Bk%5D\"$ implies $\"P%5Bk%2B1%5D\"$
\n" ); document.write( "in this case...
\n" ); document.write( " $\"S%5Bn%5D+%2B+a%5Bn%2B1%5D+=+S%5Bn%2B1%5D\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"n%5E2%2B2n%2B1=%28n%2B1%29\"$ \r
\n" ); document.write( "\n" ); document.write( "true so we are done (it must be true for all n)\r
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