What is the sum from n=0 to infinity of (sin(1/n))/n ?

The sum from n=0 to infinity of (sin(1/n))/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=0 to infinity of (sin(1/n))/n

n = 0 \sum \infty \frac{sin ( \frac{1}{n} )}{n}

converges

Solution steps

n = 1 \sum \infty \frac{sin ( \frac{1}{n} )}{n}

Apply Series Integral Test:

converges

= converges

n = 0 \sum \infty 3 + 15 + 75 + 375

n = 1 \sum \infty \frac{5}{2 ^{n - 2}}

n = 1 \sum \infty \frac{1}{( n + 2 ) ^{3}}

k = 0 \sum \infty \frac{1}{100 + k}

n = 1 \sum \infty (- 1)^{n} n^{3}

What is the sum from n=0 to infinity of (sin(1/n))/n ?
The sum from n=0 to infinity of (sin(1/n))/n is converges