2.7182818284590452353602874713526624977572470936999595749669676277...

e is a transcendental number

[2; 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, 1, 1, 10, 1, 1, 12, 1, 1, 14, 1, 1, 16, 1, 1, 18, 1, ...]

e = e^z for z = 1

e = sum_(k=0)^∞ 1/(k!)

e = sum_(k=0)^∞ (k - 1)^2/(k!)

e = sum_(k=0)^∞ (2 k + 1)/((2 k)!)