SOLUTION: i) 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 t

Question 894440: i) 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 by jibirajeev(1) (Show Source): You can put this solution on YOUR website!
My definition p(n)=p(n-1)+1
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
= 4(n+1)+7=4n+11
RELATED QUESTIONS
If E is the set of even integers, P is the set of positive integers, and F is the set of... (answered by palanisamy)

If E is the set of even intergers, P is the set of positive integers, and F is the set of (answered by stanbon)

Which of the following describes the union of the set of integers less than √20 and (answered by oscargut)

Find all sets of four consecutive positive integers such that the greatest integer in the (answered by dfrazzetto)

I need to find all sets of three consecutive positive even integers with a sum no greater (answered by tommyt3rd)

Set A consists of all integers a such that a = p2 � 1, where p is a prime greater than 3. (answered by robertb)

Write down a recursive definition of the geometric sequence that has 1st term a and... (answered by Edwin McCravy)

Please help me solve this problem:find all sets of tow consecutive positive odd integers... (answered by ankor@dixie-net.com)

If p and r are positive integers and 2p + r -1 = 2r + p + 1, which of the following must... (answered by rapaljer)