## Excel in math and science

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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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TopNewestHint : Induction. :)

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As Zi Song has pointed out, direct induction is one of the easiest ways to go. You can also recognize that \[a_{n} = a_{n-1} \times \left(10^{2 \cdot 3^n} + 10^{3^n} + 1 \right) = a_{n-1} \times \left( \left(10^{3^n} \right)^2 + 10^{3^n} + 1\right)\] It should be easy to show that \(3\) divides \(\left( \left(10^{3^n} \right)^2 + 10^{3^n} + 1\right)\). Hence, you can now conclude that \(3a_{n-1}\) divides \(a_n\).

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I came to the same solution as that of Marvis N. Question's not difficult, just presence of mind is needed!

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this type of questions i often come across

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but i think solution may be somehow critical

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I DONT NOTHING ABOUT HOW TO SOLVE THIS

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