Find the sum of n terms of the series $(4 - \frac{1}{n}) + (4 - \frac{2}{n}) + (4 - \frac{3}{n}) +$ ........

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Solution

$\Rightarrow (4 + 4 + 4 + . . . . . . n t i m e s) + (\frac{1}{n} + \frac{2}{n} + \frac{3}{n} + . . . . . . + \frac{n}{n})$

$\Rightarrow 4 n + \frac{1}{n} (1 + 2 + 3 + . . . . + n)$

$\Rightarrow 4 n + \frac{1}{n} \frac{n (n + 1)}{2}$

$\Rightarrow 4 n + \frac{n + 1}{2}$

$\Rightarrow \frac{9 n + 1}{2}$

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