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why does nn12 work. For the proof we will count the number of dots in Tn but instead of summing the numbers 1 2 3 etc up to n we will find the total using only one. Dots in triangle nn12.
Step 2 is best done this way. Show it is true for first case usually n1. As an integer then we have that n1.
Now it is easy to work out how many dots.
Since there are N-1 items there are N-12 such pairs. We just note. How to Do it. Now it is easy to work out how many dots.