+132 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!
