What is the sum from k=1 to infinity of 1/(1+k^2) ?

The sum from k=1 to infinity of 1/(1+k^2) is converges

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sum from k=1 to infinity of 1/(1+k^2)

k = 1 \sum \infty \frac{1}{1 + k ^{2}}

converges

Solution steps

k = 1 \sum \infty \frac{1}{1 + k ^{2}}

Apply Series Comparison Test:

converges

= converges

f (x) = x^{5} - 2 x^{3} + x - 1

\frac{d}{d x} (\frac{6 x + 2 x ^{2}}{( 3 + 2 x ) ^{2}})

\int_{- 1}^{3} x^{2} + 6 x + 3 d x

x \to 2 + lim (3 - a x - x^{2})

\int \frac{7 - x}{( x - 2 ) ^{2}} d x

What is the sum from k=1 to infinity of 1/(1+k^2) ?
The sum from k=1 to infinity of 1/(1+k^2) is converges