What is the sum from n=1 to infinity of (5^n)/(6^n) ?

The sum from n=1 to infinity of (5^n)/(6^n) is 5

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sum from n=1 to infinity of (5^n)/(6^n)

n = 1 \sum \infty \frac{5 ^{n}}{6 ^{n}}

5

Solution steps

n = 1 \sum \infty \frac{5 ^{n}}{6 ^{n}}

Apply exponent rule:

\frac{a ^{c}}{b ^{c}} = (\frac{a}{b})^{c}

= n = 1 \sum \infty (\frac{5}{6})^{n}

n = k \sum \infty (a_{n}) = n = 0 \sum \infty (a_{n}) - a_{0} - a_{1} - \dots a_{k - 1}

= n = 0 \sum \infty (\frac{5}{6})^{n} - (\frac{5}{6})^{0}

n = 0 \sum \infty (\frac{5}{6})^{n} = 6

= 6 - (\frac{5}{6})^{0}

Simplify

= 5

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What is the sum from n=1 to infinity of (5^n)/(6^n) ?
The sum from n=1 to infinity of (5^n)/(6^n) is 5