What is the sum from n=3 to infinity of 1/(5^n-3^n) ?

The sum from n=3 to infinity of 1/(5^n-3^n) is converges

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sum from n=3 to infinity of 1/(5^n-3^n)

n = 3 \sum \infty \frac{1}{5 ^{n} - 3 ^{n}}

converges

Solution steps

n = 3 \sum \infty \frac{1}{5 ^{n} - 3 ^{n}}

Apply Series Ratio Test:

converges

= converges

k = 5 \sum \infty \frac{1}{( k - 4 ) ^{5}}

k = 0 \sum \infty (- \frac{1}{8})^{k}

n = 1 \sum \infty 1 - (- 1)^{n}

n = 0 \sum \infty cos (\frac{18}{n})

n = 3 \sum \infty \frac{5}{n ^{3}}

What is the sum from n=3 to infinity of 1/(5^n-3^n) ?
The sum from n=3 to infinity of 1/(5^n-3^n) is converges