# Pascal's Triangle Representation

(See attached file for full problem description)

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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:

Row 5: 1 5 10 10 5 1

So, S_(5,0) = 1 + 10 = 11

S_(5,1) = 5 + 5 = 10

S_(5,2) = 10 + 1 = 10

Row 6: 1 6 15 20 15 6 1

So, S_(6,0) = 1 + 20 + 1 = 22

S_(5,1) = 6 + 15 = 21

S_(5,2) = 15 + 6 = 21

Find S_(100,1). Generalize

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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https://brainmass.com/math/triangles/pascals-triangle-representation-60996

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#### Solution Summary

The expert examines Pascal's triangle representations. The third elements in the nth row of Pascal's Triangles beginning on the left are determined.