document.write( "Question 144244: PLEASE HELP ASAP
\n" ); document.write( "In using mathematical induction to prove 8+10+12+...+(2n+6) = n^2+7n, the P k+1 statement is 8+10+12+...+(2k+6) = (k+1)+7(k+1)
\n" ); document.write( "Is this true or false
\n" ); document.write( "THANK YOU \n" ); document.write( "
Algebra.Com's Answer #105036 by stanbon(75887)\"\" \"About 
You can put this solution on YOUR website!
In using mathematical induction to prove 8+10+12+...+(2n+6) = n^2+7n, the
\n" ); document.write( "P(k+1) statement is 8+10+12+...+(2k+6) + 2(k+1)+ 6 = (k+1)^2+7(k+1)
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\n" ); document.write( "Assume P(k)= 8 + 10 + ...+2k+6 = k^2+7k is true\r
\n" ); document.write( "\n" ); document.write( "Show that P(k+1) = 8+10+12+...+(2k+6) + (2(k+1)+6) = (k+1)^2 + 7(k+1)
\n" ); document.write( "Substituting on the left side you get:
\n" ); document.write( "P(K) +2(k+1) + 6
\n" ); document.write( "= k^2+7k + 2(k+1)+6
\n" ); document.write( "= k^2+ 2x+8 + 7k
\n" ); document.write( "= k^2 + 2x + 1 + 7k+7
\n" ); document.write( "= (k+1)^2 + 7(k+1)
\n" ); document.write( "--------
\n" ); document.write( "So the form is true for all k.
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.\r
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