As The Limit of A Sequence
The number e is equal to the limit of several infinite sequences:
- and
- (both by Stirling's formula).
The symmetric limit,
may be obtained by manipulation of the basic limit definition of e. Another limit is
where is the nth prime and is the primorial of the nth prime.
where is the prime counting function. This definition is a direct corollary of the prime number theorem.
Also:
In the special case that, the result is the famous statement:
Read more about this topic: List Of Representations Of E
Famous quotes containing the words limit and/or sequence:
“Can you find out the deep things of God? Can you find out the limit of the Almighty?”
—Bible: Hebrew, Job 11:7.
“It isn’t that you subordinate your ideas to the force of the facts in autobiography but that you construct a sequence of stories to bind up the facts with a persuasive hypothesis that unravels your history’s meaning.”
—Philip Roth (b. 1933)