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


Al P. answered • 02/26/18

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