e = 1+ 1/1 + 1/(2*1) + 1/(3*2*1) + 1/(4*3*2*1) + 1/(5!)+ 1/(6!) + * * *e=1+11+12⋅1+13⋅2⋅1+14⋅3⋅2⋅1+15!+16!+⋅⋅⋅
(For positive integer nn, we define: n! = n(n-1)(n-2) * * * (3)(2)(1)n!=n(n−1)(n−2)⋅⋅⋅(3)(2)(1) and 0! = 10!=1
ee is the coordinate on the xx-axis where the area under y=1/xy=1x and above the axis, from 11 to ee is 11
e = lim_(m rarr oo) (1+1/m)^m
e ~~ 2.71828 it is an irrational number, so its decimal expansion neither terminates nor goes into a cycle.
(It is also transcendental which, among other things, means it cannot be written using finitely many algebraic operations
(xx, -: , +, -, "exponents and roots") and whole numbers.)
