The expression \[ S=n^{2}\left(\frac{C_{0}}{C_{1}}\right)+(n-1)^{2}...

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The expression
\[
S=n^{2}\left(\frac{C_{0}}{C_{1}}\right)+(n-1)^{2}\left(\frac{C_{1}}{C_{2}}\right)+\cdots+1^{2}\left(\frac{C_{n-1}}{C_{n}}\right)
\]
equals
(a) \( \frac{1}{6} n(n+1)(2 n+1) \)
(b) \( \frac{1}{6} n(n+1)(n+2) \)
(c) \( \frac{1}{3} n(n+1)(n+2) \)
(d) none of these
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