If 3 + 3α + 3{α ^2} + .........∞ = frac{{45}}{8} , then value of α will be

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8. Sequences and Series

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

A

$15/23$

B

$7/15$

C

$7/8$

D

$15/7$

Solution

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

Standard 11

Mathematics

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