Prove by induction where n is a positive integer: The greatest number of regions that n straight lines can divide a circle is The problem is, I do not know where/how to start. Can someone give me some hints to begin?
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Always start by proving that it starts. Try n = 1 and see. Try n = 2 and convince yourself. Is it really 4? Try n = 3 and become a disciple. Is it really 7? Are we really proving the premise or just the equation?
Show for n=1: ........true. Assume is true. This the induction hypothesis is We must show is true. If we add a (k+1)st line, the regions increase by k+1. This shows that is true and the induction holds. QED.
Thanks. So we are proving just proving the equation.
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