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If \( a_{0}, a_{1}, a_{2}, \ldots a_{n} \) is an arithmetic progression of positive integers, then to evaluate
\( \frac{C_{0}}{a_{0}} \pm \frac{C_{1}}{a_{1}}+\frac{C_{2}}{a_{2}} \pm \cdots \) upto \( (n+1) \) terms, we integrate both the sides of
\[
\sum_{r=0}^{n} C_{r} x^{r}=(1+x)^{n}
\]
after multiplying by \( x^{r} \) for an appropriate value of \( r \).
\( -\frac{1}{2} C_{1}-\frac{2}{3} C_{2}+\frac{3}{4} C_{3}-\ldots \) upto \( n \) terms equals
(a) \( \frac{1}{n+1} \)
(b) \( \frac{1}{2 n+1} \)
(c) \( \frac{2}{n+1} \)
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