Upto Infinite!

Algebra Level 1

1 − 1 3 + 1 3 2 − 1 3 3 + . . . . . ∞ = ? 1-\frac{1}{3}+\frac{1}{3^2}-\frac{1}{3^3}+.....\infty=?


The answer is 0.75.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Akshat Sharda
Oct 30, 2015

1 − 1 3 + 1 3 2 − 1 3 3 + . . . . . ∞ = 1 1 + 1 3 = 3 4 = 0.75 1-\frac{1}{3}+\frac{1}{3^2}-\frac{1}{3^3}+.....\infty=\frac{1}{1+\frac{1}{3}}=\frac{3}{4}=\boxed{0.75}

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Can u please explain it how to u get 1 + 1 3 1+\frac{1}{3} in denominator.

A Former Brilliant Member - 5 years, 7 months ago

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1 1 − ( − 1 3 ) = 1 1 + 1 3 \frac{1}{1-\left(-\frac{1}{3}\right)}=\frac{1}{1+\frac{1}{3}}

Its just the infinite G.P. sum. See more here .

Akshat Sharda - 5 years, 7 months ago

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