Question

The sum $\sum _{x=0}^{\infty }\frac{1}{x^2+5x+4}$ is equal to

• A. $\frac{37}{90}$
• B. $\frac{19}{36}$
• C. $\frac{11}{18}$
• D. $\frac{13}{24}$

Answer 1

Answer: (C)

$\frac{1}{3}\sum _{x=0}^{\infty }\left(\frac{1}{x+1}-\frac{1}{x+4}\right)$
Substituting $0,1,2,3,\dots \dots \infty$, we get $=\frac{11}{18}$