#### Harmonic

```"""
Harmonic mean
Reference: https://en.wikipedia.org/wiki/Harmonic_mean

Harmonic series
Reference: https://en.wikipedia.org/wiki/Harmonic_series(mathematics)
"""

def is_harmonic_series(series: list) -> bool:
"""
checking whether the input series is arithmetic series or not
>>> is_harmonic_series([ 1, 2/3, 1/2, 2/5, 1/3])
True
>>> is_harmonic_series([ 1, 2/3, 2/5, 1/3])
False
>>> is_harmonic_series([1, 2, 3])
False
>>> is_harmonic_series([1/2, 1/3, 1/4])
True
>>> is_harmonic_series([2/5, 2/10, 2/15, 2/20, 2/25])
True
>>> is_harmonic_series(4)
Traceback (most recent call last):
...
ValueError: Input series is not valid, valid series - [1, 2/3, 2]
>>> is_harmonic_series([])
Traceback (most recent call last):
...
ValueError: Input list must be a non empty list
>>> is_harmonic_series()
Traceback (most recent call last):
...
ValueError: Input series cannot have 0 as an element
>>> is_harmonic_series([1,2,0,6])
Traceback (most recent call last):
...
ValueError: Input series cannot have 0 as an element
"""
if not isinstance(series, list):
raise ValueError("Input series is not valid, valid series - [1, 2/3, 2]")
if len(series) == 0:
raise ValueError("Input list must be a non empty list")
if len(series) == 1 and series != 0:
return True
rec_series = []
series_len = len(series)
for i in range(0, series_len):
if series[i] == 0:
raise ValueError("Input series cannot have 0 as an element")
rec_series.append(1 / series[i])
common_diff = rec_series - rec_series
for index in range(2, series_len):
if rec_series[index] - rec_series[index - 1] != common_diff:
return False
return True

def harmonic_mean(series: list) -> float:
"""
return the harmonic mean of series

>>> harmonic_mean([1, 4, 4])
2.0
>>> harmonic_mean([3, 6, 9, 12])
5.759999999999999
>>> harmonic_mean(4)
Traceback (most recent call last):
...
ValueError: Input series is not valid, valid series - [2, 4, 6]
>>> harmonic_mean([1, 2, 3])
1.6363636363636365
>>> harmonic_mean([])
Traceback (most recent call last):
...
ValueError: Input list must be a non empty list

"""
if not isinstance(series, list):
raise ValueError("Input series is not valid, valid series - [2, 4, 6]")
if len(series) == 0:
raise ValueError("Input list must be a non empty list")
for val in series:  