Find an Online Tutor Now

Lounie G.

asked • 02/25/18

Induction proofs

Exercise 2.25: P(n) is the number of regions in the plane formed by n lines in general position: n=1, p(n)=2; n=2, p(n)=4; n=3, p(n)=7; n=4, p(n)=11; n=5, p(n)=16; n=6, p(n)=22.

2.76) Finish the process begun in 2.25, where it's outlined how experimentation might lead to the conjecture that n line in general position divide the plane into p(n) pieces, with p(1)=2 and p(n) = p(n-1)+n for n>=2. First write down the details of the induction argument; then write the work in theorem-proof style that suitable for others to read.

2.87) prove that p(n)=n^2+n+2/2 is a non-recursive solution to the lines in the plane problem of 2.25 and 2.76.

1 Expert Answer

By:

Al P. answered • 02/26/18

Tutor
New to Wyzant

Online Mathematics tutor

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.