পাশের ধারাটির n-তম পদ পর্যন্ত যােগফল নির্ণয় কর:

  $\frac{14}{1.4 . 2.5} + \frac{68}{4.7 . 5.8} + \frac{158}{7.10 . 8.11} + \ldots \ldots . .$  

$u_{n}=\frac{18 n^{2}-4}{\left(9 n^{2}+3 n-2\right)\left(9 n^{2}-3 n-2\right)}=\frac{\left(9 n^{2}+3 n-2\right)+\left(9 n^{2}-3 n-2\right)}{\left(9 n^{2}+3 n-2\right)\left(9 n^{2}-3 n-2\right)}=\frac{1}{\left(9 n^{2}-3 n-2\right)}+\frac{1}{\left(9 n^{2}+3 n-2\right)}$

$\begin{array}{l} =\frac{1}{(3 n=1)(3 n+2)}+\frac{1}{(3 n+1)(3 n-2)} \Rightarrow S_{n}=c-\frac{1}{3(3 n-1)}-\frac{1}{3(3 n-2)} \Rightarrow \frac{14}{1 \times 4 \times 2 \times 5}=c-\frac{1}{3.2}-\frac{1}{3.1} \\ \therefore c=\frac{17}{20} \quad \therefore S_{n}=\frac{17}{20}-\frac{1}{3(3 n-1)}-\frac{1}{3(3 n-2)} \end{array}$