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What is the value of :

\((0.05)^{\log_\sqrt{20} (0.1+0.01+0.001..............\infty)}\)

Note by Snehdeep Arora 4 years, 7 months ago

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First we sum the infinite geometric series with first term 0.1, common ratio 0.1 We get S = 0.1/(1-0.1) = 1/9. Take 0.05 = 1/20 = (√20)^-2, then the term can be resolved to 81. (Sorry can't show expression by typing)

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yeah

81

Is the answer 81?

correct

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Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

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TopNewestFirst we sum the infinite geometric series with first term 0.1, common ratio 0.1 We get S = 0.1/(1-0.1) = 1/9. Take 0.05 = 1/20 = (√20)^-2, then the term can be resolved to 81. (Sorry can't show expression by typing)

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yeah

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81

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81

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Is the answer 81?

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correct

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