回復 1# shmilyho 的帖子
\(\begin{align}
& \frac{k+4}{k\left( k+1 \right)\left( k+2 \right)} \\
& =\frac{k+2+2}{k\left( k+1 \right)\left( k+2 \right)} \\
& =\frac{k+2}{k\left( k+1 \right)\left( k+2 \right)}+\frac{2}{k\left( k+1 \right)\left( k+2 \right)} \\
& =\frac{1}{k\left( k+1 \right)}+\frac{2}{k\left( k+1 \right)\left( k+2 \right)} \\
& =\left( \frac{1}{k}-\frac{1}{k+1} \right)+\left( \frac{1}{k\left( k+1 \right)}-\frac{1}{\left( k+1 \right)\left( k+2 \right)} \right) \\
\end{align}\)
