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HW Problem 1.28

 
 
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HW Problem 1.28
by Carol W - Tuesday, 19 September 2017, 8:12 PM
 

For HW question number 28, I do not understand the explanation for the problem. How does the worded part translate to "Therefore the answer is 2+2+3+4+5+6=222+2+3+4+5+6=22." ?

 
Picture of David Reynoso
Re: HW Problem 1.28
by David Reynoso - Wednesday, 20 September 2017, 10:02 AM
 

Every time a new line is added, there are as many new regions as the number of lines: With one line there were $2$ regions; with two lines there were $2$ new regions for a total of $2+2 = 4$; with $3$ lines there were $3$ new regions for a total of $2+2+3 = 7$. Continuing this way, when we have $6$ lines there will be $2+2+3+4+5+6 = 22$ regions.

 
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