from functools import lru_cache
import math

@lru_cache(maxsize = None)
def fib(n):
    if n <=1:
        return n
    return fib(n-1)+fib(n-2)


def derivative(func, delta = 0.000001):
    def df(x):
        return (func(x+delta)-func(x-delta))/(2*delta)
    return df

def harmonic(n):
    if n<1:
        print("Error: argument should be larger than 0")
    accu = 0.0
    for i in range(1, n+1):
        accu += 1/i
    return accu
    
def grade(number):
    if number < 0 or number > 100:
        print("Error: your argument is not in the expected range")
    if number >= 90:
        return 'A'
    if number >=80:
        return 'B'
    if number >= 65:
        return 'C'
    if number >= 55:
        return 'D'
    return 'F'