If Hn=1+12+13+…+1n then value of 1+32+53+…+2n−1nis

A
$H_{n} + n$
B
$2 n - H_{n}$
C
$n - 1 + H_{n}$
D
$H_{n} + 2 n$

Solution:

$\begin{array}{l} 1 + \frac{3}{2} + \frac{5}{3} + \dots + \frac{2 n - 1}{n} \\ = (2 - 1) + (2 - \frac{1}{2}) + (2 - \frac{1}{3}) + \dots + (2 - \frac{1}{n}) \\ = 2 n - H_{n} \end{array}$

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