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OpenStudy (anonymous):
1) give a recursive definition of the set P of all positive integers greater than 0 II) formulate tha appropriate induction principle III) use mathematical induction to prove that 11+15+19 +... + (4n+7) = 2n^2 + 9n for all positive n>0
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OpenStudy (dan815):
p(n)=p(n-1)+1
OpenStudy (dan815):
11+15+19..+(4n+7)+(4(n+1)+7)=2(n+1)^2+9(n+1) =2(n^2+2n+1)+9n+1 =2n^2+9n + 4n+2+9=2n^2+9n + 4n+11 therefore works for the step up case
OpenStudy (dan815):
as 4(n+1)+7=4n+11
OpenStudy (anonymous):
so both sides are equal.
OpenStudy (anonymous):
Thank you very much
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OpenStudy (midhun.madhu1987):
As an additional information, please find the attached file. It contains the steps to solve Mathematical Induction Problems...
OpenStudy (anonymous):
wow! its real help .. thanks much appreciated
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