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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