First slide

Arithmetico-Geometric Progression

Question

$1 + \frac{3}{2} + \frac{5}{2^{2}} + \frac{7}{2^{3}} \dots \infty$ is equal to

Moderate

A

3
B

6
C

9
D

12

Solution

This progression is an arithmetico-geometric series.
$\begin{array}{l} ∴ S_{\infty} = \frac{a}{1 - r} + \frac{dr}{(1 - r)^{2}} \\ = \frac{1}{1 - 1 / 2} + \frac{2}{(1 - 1 / 2)^{2}} \\ = \frac{2}{1 / 2} + \frac{2}{1 / 4} = 4 + 8 = 12 \end{array}$

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