Question

Find the sum of series 1+cos theta cos theta+cos 2 theta cos square theta+cos 3 theta cos cube theta...

Answer 1

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Answer 2

The sum of series $1+\cos \theta+\cos^2 \theta+\cos^3 \theta+\cos^4 \theta+ ....... +\infty$ $=\dfrac{1}{1-\cos \theta}$

Step-by-step explanation:

The given sum of series:

$1+\cos \theta+\cos^2 \theta+\cos^3 \theta+\cos^4 \theta+ ....... +\infty$

The given sequence are in GP.

Here, first term(a) = 1 and common ratio(r) = $\dfrac{\cos \theta}{1} =\cos \theta$

To find, the sum of  the given series = ?

We know that,

The sum of infinite term of GP = $\dfrac{a}{1-r}$

$1+\cos \theta+\cos^2 \theta+\cos^3 \theta+\cos^4 \theta+ ....... +\infty$

$=\dfrac{1}{1-\cos \theta}$

∴ The sum of series $1+\cos \theta+\cos^2 \theta+\cos^3 \theta+\cos^4 \theta+ ....... +\infty$ $=\dfrac{1}{1-\cos \theta}$