Multiple choice

The sum up to $9$ terms of the series $\displaystyle \frac{1}{2}+\frac{1}{3}+\frac{1}{6}+ ...$ is

  1. $\displaystyle -\frac{5}{6}$
  2. $\displaystyle -\frac{1}{2}$
  3. $1$
  4. $\displaystyle -\frac{3}{2}$
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D Correct answer
AI explanation

The difference between consecutive terms is -1/6, making this an arithmetic progression with first term 1/2 and common difference -1/6. Using the sum formula for an arithmetic progression, S = n/2 times (2a + (n-1)d), we get S = 9/2 times (2(1/2) + (9-1)(-1/6)). This simplifies to 9/2 times (1 - 4/3), which equals 9/2 times (-1/3), resulting in a sum of -3/2.

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