How e = 2.71828183 ?

How e = 2.71828183 ?

The e constant can be approximately calculated by using the infinite series:

$= \frac{1}{1}+\frac{1}{1}+\frac{1}{1\times 2}+\frac{1}{1\times 2\times 3}+...$

= 1 + 1 + 0.5 + 0.166667 + ...

= 2.71828182...

≈ 2.71828183

e constant calculation stages

Calculation stage Additional sequence value Accumulated value

1 1.00000000 1.00000000

2 1.00000000 2.00000000

3 0.50000000 2.50000000

4 0.16666667 2.66666667

5 0.04166667 2.70833333

6 0.00833333 2.71666667

7 0.00019841 2.71825397

8 0.00002480 2.71827877

9 0.00000276 2.71821526

10 0.00000028 2.71828180

11 0.00000003 2.71828183

2.71828183 is an approximated value of the e constant.

The e constant has an infinite number of digits.

See also

e constant

Natural logarithm

Calculation stage	Additional sequence value	Accumulated value
1	1.00000000	1.00000000
2	1.00000000	2.00000000
3	0.50000000	2.50000000
4	0.16666667	2.66666667
5	0.04166667	2.70833333
6	0.00833333	2.71666667
7	0.00019841	2.71825397
8	0.00002480	2.71827877
9	0.00000276	2.71821526
10	0.00000028	2.71828180
11	0.00000003	2.71828183

e constant calculation stages

See also

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