Multiple choice

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

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

The series is an arithmetic progression where the first term is 1/2 and the common difference is -1/6. Using the sum formula for an arithmetic progression, the sum of the first 9 terms is S = 9/2 * [2(1/2) + (9 - 1)(-1/6)]. Inside the brackets, we calculate 1 - 8/6, which equals -1/3. Multiplying this by 9/2 gives the final sum of -3/2.

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