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Find the Sum of the Following Geometric Series: √ 2 + 1 √ 2 + 1 2 √ 2 + . . . to 8 Terms ; - Mathematics

Find the sum of the following geometric series:

\[\sqrt{2} + \frac{1}{\sqrt{2}} + \frac{1}{2\sqrt{2}} + . . .\text { to 8  terms };\]

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Solution

Here, a = \[\sqrt{2}\] and r = \[\frac{1}{2}\] .

\[S_8 = a\left( \frac{1 - r^8}{1 - r} \right)\]

\[ = \sqrt{2}\left( \frac{1 - \left( \frac{1}{2} \right)^8}{1 - \frac{1}{2}} \right)\]

\[ = \sqrt{2}\left( \frac{1 - \frac{1}{256}}{\frac{1}{2}} \right)\]

\[ = 2\sqrt{2}\left( \frac{255}{256} \right)\]

\[ = \frac{255\sqrt{2}}{128}\]

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 20 Geometric Progression
Exercise 20.3 | Q 2.2 | Page 27
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