The sum to infinity of the progression 9 - 3 + 1 - 1 3 + ..... is - Vidyadip

MCQ

The sum to infinity of the progression $9 - 3 + 1 - \frac{1}{3} + .....$ is

A
$9$
B
$9/2$
✓
$27/4$
D
$15/2$

✓

Answer

Correct option: C.

$27/4$

c
(c) Infinite series $9 - 3 + 1 - \frac{1}{3}......\infty $ is a

$G.P.$ with $a = 9,r = \frac{{ - 1}}{3}$

${S_\infty } = \frac{a}{{1 - r}} = \frac{9}{{1 + \left( {\frac{1}{3}} \right)}} = \frac{{9 \times 3}}{4} = \frac{{27}}{4}$.

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