First slide

Geometric progression

Question

$If x = 30^{\circ} then the sum of the series 1 + \cos 2 x + \cos^{2} 2 x + \dots + \infty is$

Moderate

A

$\infty$
B

4
C

2
D

1

Solution

$\begin{array}{l} 1 + \cos 60 + \cos^{2} 60 + \dots \\ = 1 + \frac{1}{2} + \frac{1}{2^{2}} + \frac{1}{2^{3}} + \dots \infty = \frac{1}{1 - 1 / 2} = 2 (\sin c e s u m o f i n f i n i t e t e r m s i n G . P = \frac{a}{1 - r}) \end{array}$

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