Calculate $\lim\limits_{n\rightarrow \infty }\sum_{k=1}^{n}\frac{6}{k(k+1)(k+3)}$

Hint

$$\frac{2}{k}-\frac{3}{k+1}+\frac{1}{k+3}=\frac{2}{k}-\frac{2}{k+1}-\frac{1}{k+1}+\frac{1}{k+3}=2\left(\frac{1}{k}-\frac{1}{k+1} \right)-\left(\frac{1}{k+1}-\frac{1}{k+3} \right)$$

Tags:

Limits

Calculus

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