Question

The harmonic mean of the numbers $1 , \frac{1}{2} , \frac{1}{3} , \frac{1}{4},...., \frac{1}{n} $ is

• A. $\frac{n + 1}{2} $
• B. $\frac{2}{n + 1} $
• C. $\frac{n}{1 +\frac{1}{2} + \frac{1}{3} + \frac{1}{4}+....+ \frac{1}{n}}$
• D. $ \frac{1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4}+....+ \frac{1}{n}}{n} $

Answer 1

Answer: (B)

Harmonic mean of $x_1, x_2, ... , x_n$ (none of which is 0)
$ = \frac{n}{\sum\left(\frac{1}{x_{i}}\right)}$
$\therefore $ Required harmonic mean
$ = \frac{n}{ 1+2+3+..+n} = \frac{2n}{n\left(n+1\right)} = \frac{2}{n+1} $