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8. Sequences and Series
easy
The sum of the series $\frac{1}{2} + \frac{1}{3} + \frac{1}{6} + ........$ to $9$ terms is
A
$ - \frac{5}{6}$
B
$ - \frac{1}{2}$
C
$1$
D
$ - \frac{3}{2}$
Solution
(d) Given series $\frac{1}{2} + \frac{1}{3} + \frac{1}{6} + ……..$
Here $a = \frac{1}{2}$, common difference $d = – \frac{1}{6}$ and $n = 9$.
$ \Rightarrow $ ${S_9} = \frac{9}{2}\left[ {2 \times \frac{1}{2} + (9 – 1)\left( { – \frac{1}{6}} \right)} \right] = – \frac{3}{2}$.
Standard 11
Mathematics
