If 3 + 3alpha + 3{alpha ^2} + dots infty = fr | 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 the formula $S = \frac{a}{1 - r}$,where $|r| Given the equation: $3 + 3\alpha + 3{\alpha ^2} + \dots \infty = \frac{45}{8}$.Substituting the values into the formula: $\frac{3}{1 - \alpha} = \frac{45}{8}$.Dividing both sides by $3$: $\frac{1}{1 - \alpha} = \frac{15}{8}$.Cross-multiplying: $8 = 15(1 - \alpha)$.$8 = 15 - 15\alpha$.$15\alpha = 15 - 8$.$15\alpha = 7$.Therefore,$\alpha = \frac{7}{15}$.

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

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