Solve for x = ? x =?

Algebra Level 2

If 1 + x + x 2 + x 3 + x 4 + ⋯ = 2018 1+x+x^2+x^3+x^4+ \dots = 2018 then x = ? \large\color{#D61F06} x=?

1009 2019 \frac{1009}{2019} 2017 2018 \frac{2017}{2018} 2018 2017 \frac{2018}{2017} 1009 2018 \frac{1009}{2018} 2018 2019 \frac{2018}{2019}

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

Tom Engelsman
Jan 29, 2018

The LHS is an infinite geometric series with common ratio x x and sum equal to 1 1 − x . \frac{1}{1-x}. Solving for x x yields:

1 1 − x = 2018 ⇒ x = 2017 2018 . \frac{1}{1-x} = 2018 \Rightarrow \boxed{x = \frac{2017}{2018}}.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Thank you Tom for sharing your solution.

Hana Wehbi - 3 years, 4 months ago

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My pleasure, Hana, as always!

tom engelsman - 3 years, 4 months ago

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I really like your solutions, replies,...etc :)

Hana Wehbi - 3 years, 4 months ago

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