Question

Find the sum of the following harmonic series: $\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...10$ terms.

Answer 1

We know the formula for sum of nth term in arithmetic progression.
The reciprocal of arithmetic progression is harmonic progression.
$a=2,d=2$
$S_n=\frac{n}{2}[2a_1+(n-1\left)d\right]$
$S_{1}0=\frac{10}{2}[2\times 2+(10-1\left)2\right]$
$S_{1}0=5[4+18]$
$S_{1}0=110$
Sum of first 10 terms of HP $=\frac{1}{110}$