How do u calculate "e"?

Answer 1

There are a couple of ways. "e" is formally defined as the limit of (1 + 1/n)^n as n→∞. So you could take increasing values of n and calcuate this out. The higher the value of n, the more accurate your approximation of e will be.

Another way is to use the following infinite sum:

1/0! + 1/1! + 1/2! + 1/3! + 1/4! + ...

Again, using more and more terms will get you a number closer and closer to e. Like all irrational numbers, calculating it becomes a quesiton of "How accurate do you want it?"

Answer 2

With a great deal of patience or a good computer. The Taylor series for e^x is
e^x = ∑ 1 + x/1 + x^2/2 + x^3/3! + x^4/4! + . . . . .
e^1 = e, so
e = ∑ 1 + 1/1 + 1/2 + 1/3! + 1/4! + . . . . .
The series converges, and you can calculate the value accurate to 9 decimal places fairly easily by hand.

Answer 3

Theres' an infinite sequence which converges to e:

lim k=1 to inf { (1+1/k)^k } , this is what stmc was alluding to.

There's also an infinite series that also converges to e:

lim n-> inf { sum k=0 to n { 1/n! } }

I once programmed these on my new, in 1975, HP 25C calculator.

It took over about 175,000 for the sequence to get to within 10^8 of e and only 12 terms in the series.

Note that the series is actually a special case of the power series for e^x, where x=1.

There are other ways to get e but they all involve convergence of infinite processes. Such numbers, like pi, that can only be obtained by an infinite number of elementary operations are called transcendental numbers. All transcendenatl numbers are irrational but not vice versa. That last result is not at all easy to prove.

If you have a TI-83 or better calculator that does sequences, it's interesting to plot the sequence and watch it converge.

Answer 4

I like the official definition, lim as n goes to infinity of (1 + 1/n)^n
It's instructive, and fun, to punch this into a calculator and see it approach e to an increasing number of sigificant figures.
And if you have a good graphics calculator that will let you enter the formula and make a table for increasing values of n, it's a lot easier to see.
Encouraging students to do things like this, and relating it to something specific, such as continuously compoundind interest, or growth in a cell culture, helps people to understand what a useful and beautful nunber "e" is.
Any time you have something that increases or decreases at a rate based on the current amount, there's an "e" lurking in there.

Answer 5

e is napierian or hyperbolic logarithms.
e=1+1+(1/2!)+(1/3!)+(1/4!)+(1/5!)+(1/6!)+(1/7!)+--------

2! means 2 factorial = 1*2
3! means 3 factorial = 1*2*3
4! means 4 factorial = 1*2*3*4
5! means 5 factorial = 1*2*3*4*5
so and so forth

Answer 6

It's the sum of (1/n!) where n is every number from 0 to infinity. It's approximately 2.71828

Answer 7

This article gives an infinite sequence that can be used to calculate e

http://en.wikipedia.org/wiki/E_(mathematical_constant)

Answer 8

(1+1/1)^1
(1+1/2)^2
(1+1/3)^3
(1+1/4)^4
and so on

value for e is approximately 2.7182818281

Answer 9

It should be on any scientific calculator