document.write( "Question 986221: Please help me with this mathematical induction question:\r
\n" ); document.write( "\n" ); document.write( "Suppose we want to use mathematical induction to prove the following statement for all positive integers n:\r
\n" ); document.write( "\n" ); document.write( "1+3+5+...+(2n-1)=n^2\r
\n" ); document.write( "\n" ); document.write( "In the induction step, we might prove that 1+3+5+...+(2k-1)=k^2 implies the statement:\r
\n" ); document.write( "\n" ); document.write( "1+3+5+...+(2k-1)+(2k+1)=?\r
\n" ); document.write( "\n" ); document.write( "What is the correct expression in the variable k for the right side?\r
\n" ); document.write( "\n" ); document.write( "Thank you for your help and time. \n" ); document.write( "
Algebra.Com's Answer #607019 by ikleyn(52777)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "For the proof of this formula\r
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\n" ); document.write( "\n" ); document.write( "1+3+5+...+(2n-1)=n^2\r
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\n" ); document.write( "\n" ); document.write( "by the method of mathematical induction see the lesson  Mathematical induction and arithmetic progressions  in this site.\r
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