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The question is
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Let S_(n,0), S_(n,1), and S_(n,2) represent the sums of every third element in the nth row of Pascal's Triangle beginning on the left. For example:

Since the Pascal triangle is a table of the coefficient of the binomial expansion of (x + y)^n, where n is a natural number, I use this information to find S_(100,1). Am I correct?

For "generalize" part, I am thinking of using induction to prove the binomial theorem (x + y)^n.

Not sure I am on the right track to solve this problem. Can you help me with details please?
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... 1010- ca.1070) in China in mid-eleventh century has invented the Pascal's triangle that was discovered independently by Blaise Pascal in France centuries later ...

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