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PROVE THIS.... THIS IS A BIT HARDER

Note by Sayan Chaudhuri
4 years, 10 months ago

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2 votes

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

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Hint : Induction. :)

Zi Song Yeoh - 4 years, 10 months ago

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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 \(a_n\).

Marvis Narasakibma - 4 years, 10 months ago

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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!

Siddharth Kumar - 4 years, 10 months ago

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this type of questions i often come across

Sayan Chaudhuri - 4 years, 10 months ago

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but i think solution may be somehow critical

Sayan Chaudhuri - 4 years, 10 months ago

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I DONT NOTHING ABOUT HOW TO SOLVE THIS

Sayan Chaudhuri - 4 years, 10 months ago

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