If 3 + 3alpha + 3alpha^2 + dots infty = frac{ | vedclass

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(B) The given series is an infinite geometric progression with the first term $a = 3$ and common ratio $r = \alpha$.The sum of an infinite geometric s

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$7/15$

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(B) The given series is an infinite geometric progression with the first term $a = 3$ and common ratio $r = \alpha$.The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$,where $|r| Given,$\frac{3}{1 - \alpha} = \frac{45}{8}$.Dividing both sides by $3$,we get $\frac{1}{1 - \alpha} = \frac{15}{8}$.Taking the reciprocal,$1 - \alpha = \frac{8}{15}$.Therefore,$\alpha = 1 - \frac{8}{15} = \frac{15 - 8}{15} = \frac{7}{15}$.

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

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