I think I did everything correctly, but the base case return None, instead of False if the value does not exists. I cannot understand why.
def binary_search(lst, value):
if len(lst) == 1:
return lst[0] == value
mid = len(lst)/2
if lst[mid] < value:
binary_search(lst[:mid], value)
elif lst[mid] > value:
binary_search(lst[mid+1:], value)
else:
return True
print binary_search([1,2,4,5], 15)