What is the sum from n=0 to infinity of 1/(n^2+5n+6) ?

The sum from n=0 to infinity of 1/(n^2+5n+6) is 1/2

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sum from n=0 to infinity of 1/(n^2+5n+6)

n = 0 \sum \infty \frac{1}{n ^{2} + 5 n + 6}

\frac{1}{2}

Solution steps

n = 0 \sum \infty \frac{1}{n ^{2} + 5 n + 6}

Apply Telescoping Series Test:

\frac{1}{2}

= \frac{1}{2}

\int (5 x^{2} + 6 + \frac{9}{x ^{2} + 1}) d x

\frac{d h}{d t} + \frac{1}{2} h = 1

\int e^{c o s (6 t)} sin (6 t) d t

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = - 4, y^{^{'}} (0) = 4

What is the sum from n=0 to infinity of 1/(n^2+5n+6) ?
The sum from n=0 to infinity of 1/(n^2+5n+6) is 1/2