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Shown below are rows 1, 2, and 3 of Pascal's triangle.

 

\( \begin{array}{ccccccc} & & 1 & & 1 & & \\ & 1 & & 2 & & 1 & \\ 1 & & 3 & & 3 & & 1 \end{array} \)


Let  \((a_i), (b_i), (c_i)\) be the sequence, from left to right, of elements in the 2005th, 2006th, and 2007th rows, respectively, with the leftmost element occurring at \(i = 0\). Compute \(\sum_{i = 0}^{2006} \frac{b_i}{c_i} - \sum_{i = 0}^{2005} \frac{a_i}{b_i}.\)
 

 

any help would be appreciated!

 Feb 5, 2021
 #1
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By the Binomial reduction formula, the answer is 2005/2.

 Feb 5, 2021

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