SOLUTION: PLEASE HELP ASAP 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) Is this true or false THANK YOU

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Question 144244: PLEASE HELP ASAP
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)
Is this true or false
THANK YOU
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
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) + 2(k+1)+ 6 = (k+1)^2+7(k+1)
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Assume P(k)= 8 + 10 + ...+2k+6 = k^2+7k is true
Show that P(k+1) = 8+10+12+...+(2k+6) + (2(k+1)+6) = (k+1)^2 + 7(k+1)
Substituting on the left side you get:
P(K) +2(k+1) + 6
= k^2+7k + 2(k+1)+6
= k^2+ 2x+8 + 7k
= k^2 + 2x + 1 + 7k+7
= (k+1)^2 + 7(k+1)
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So the form is true for all k.
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Cheers,
Stan H.