What is the sum from n=1 to infinity of 2/(n^2+5n+6) ?

The sum from n=1 to infinity of 2/(n^2+5n+6) is 2/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sum from n=1 to infinity of 2/(n^2+5n+6)

n = 1 \sum \infty \frac{2}{n ^{2} + 5 n + 6}

\frac{2}{3}

Solution steps

n = 1 \sum \infty \frac{2}{n ^{2} + 5 n + 6}

Apply the constant multiplication rule:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

= 2 \cdot n = 1 \sum \infty \frac{1}{n ^{2} + 5 n + 6}

Apply Telescoping Series Test:

\frac{1}{3}

= 2 \cdot \frac{1}{3}

Simplify

2 \cdot \frac{1}{3} : \frac{2}{3}

= \frac{2}{3}

\int_{1}^{2} 2 π x (\frac{e ^{x}}{x}) d x

\int \frac{( x ^{2} )}{1 - x ^{2}} d x

f (x) = x^{3} - 3 x + 1, at x = 4

\frac{d}{d x} (ln (x) + 1)

\int (x^{2} + 7) ln (x) d x

What is the sum from n=1 to infinity of 2/(n^2+5n+6) ?
The sum from n=1 to infinity of 2/(n^2+5n+6) is 2/3