Find the sum of the series 1-12-122-123-

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Standard XII

Mathematics

Sufficient Condition for an Extrema

Find the sum ...

Question

Find the sum of the series $1 + \frac{1}{2} + \frac{1}{2^{2}} + \frac{1}{2^{3}} + . . . . + \infty$ .

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Solution

Given sum of series is $1 + \frac{1}{2} + \frac{1}{2^{2}} + \frac{1}{2^{3}} + \dots \infty$
Given series is the sum of the infinite $G P$ with common ratio $\frac{1}{2}$
Sum is $1 + \frac{1}{2} + \frac{1}{2^{2}} + \frac{1}{2^{3}} + \dots \infty = \frac{1}{1 - \frac{1}{2}} = \frac{1}{\frac{1}{2}} = 2$

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Find the sum of the series 1+12+122+123+....+∞.

Given sum of series is 1+12+122+123+⋯∞Given series is the sum of the infinite GP with common ratio 12Sum is 1+12+122+123+⋯∞=11−12=112=2

Find the sum of the series $1 + \frac{1}{2} + \frac{1}{2^{2}} + \frac{1}{2^{3}} + . . . . + \infty$ .