SOLUTION: using mathematical induction to prove 8+10+12+...+(2n+6) = n^2 +7n , the Pk + 1 statement is 8+10+12+...+(2n+6) = (k+1)+7(k+1)

Question 353951: using mathematical induction to prove 8+10+12+...+(2n+6) = n^2 +7n , the Pk + 1 statement is 8+10+12+...+(2n+6) = (k+1)+7(k+1)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
using mathematical induction to prove
8+10+12+...+(2n+6) = n^2 +7n ,
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Check for n=1
8 = 1^2+7*1
8 = 8
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Assume the formula is true for n = k
8+10+12+...+(2k+6) = k^2+7k
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Prove the formula is true for n = k+1
[8+10+12+...+(2k+6)]+(2(k+1)+6) = [k^2+7k] + (2(k+1)+6
= k^2+7k+2k+8
= k^2+2k+1+7k+7
= (k+1)^2+7(k+1)
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Therefore the formula is true for all positive whole numbers.
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Cheers,
Stan H.
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