Question

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

Answer 1

p(n)=p(n-1)+1

Answer 2

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

Answer 3

as 4(n+1)+7=4n+11

Answer 4

so both sides are equal.

Answer 5

Thank you very much

Answer 6

As an additional information, please find the attached file. It contains the steps to solve Mathematical Induction Problems...

Answer 7

wow! its real help .. thanks much appreciated