structural:expansion
Natural logarithm base e

∑ n = 0 ∞ (− 1) n n ! = 1 − 1 1 ! + 1 2 ! − 1 3 ! + ⋯ = 1 e {\displaystyle \sum _{n=0}^{\infty }{\frac {(-1)^{n}}{n!}}=1-{\frac {1}{1!}}+{\frac {1}{2!}}-{\frac {1}{3!}}+\cdots ={\frac {1}{e}}}

∑ n = 0 ∞ 1 n ! = 1 0 ! + 1 1 ! + 1 2 ! + 1 3 ! + 1 4 ! + ⋯ = e {\displaystyle \sum _{n=0}^{\infty }{\frac {1}{n!}}={\frac {1}{0!}}+{\frac {1}{1!}}+{\frac {1}{2!}}+{\frac {1}{3!}}+{\frac {1}{4!}}+\cdots =e}