Multiple choice

The sum to $(n+1)$ terms of the series $\displaystyle \frac{C_0}{2} - \frac{C_1}{3} + \frac{C_2}{4} - \frac{C_3}{5} +\cdots$ is

  1. $ \dfrac{1}{n+1} $
  2. $ \dfrac{1}{n+2} $
  3. $ \dfrac{1}{n(n+1)} $
  4. $ \dfrac{1}{(n+1)(n+2)} $
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D Correct answer
Explanation

The series is a sum of terms of the form ((-1)^k * C_k) / (k+2). Using the identity integral from 0 to 1 of x^k * (1-x)^n dx = n! * k! / (n+k+1)!, one can evaluate this sum. The result is 1 / ((n+1)(n+2)).

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