If 3 + 3 + 3 ^2 + ......... = 45 8 , then the value of will be - Vidyadip

MCQ

If $3 + 3\alpha + 3{\alpha ^2} + .........\infty = \frac{{45}}{8}$, then the value of $\alpha $ will be

A
$15/23$
✓
$7/15$
C
$7/8$
D
$15/7$

✓

Answer

Correct option: B.

$7/15$

b
(b) $3 + 3\alpha + 3{\alpha ^2} + 3{\alpha ^3} + ..............\infty = \frac{{45}}{8}$

$ \Rightarrow $ $3\left[ {\frac{1}{{1 - \alpha }}} \right] = \frac{{45}}{8}$

$ \Rightarrow $ $8 = 15(1 - \alpha )$

$ \Rightarrow $ $\alpha = \frac{7}{{15}}$.

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