section_path: Representations
section_name: Representations
paragraph_text: Representations
  
  The number e can be represented in a variety of ways: as an infinite series, an infinite product, a continued fraction, or a limit of a sequence. In addition to the limit and the series given above, there is also the continued fraction
  
  which written out looks like
  
  The following infinite product evaluates to e: e = 2 1 (4 3) 1 / 2 (6 ⋅ 8 5 ⋅ 7) 1 / 4 (10 ⋅ 12 ⋅ 14 ⋅ 16 9 ⋅ 11 ⋅ 13 ⋅ 15) 1 / 8 ⋯. {\displaystyle e={\frac {2}{1}}\left({\frac {4}{3}}\right)^{1/2}\left({\frac {6\cdot 8}{5\cdot 7}}\right)^{1/4}\left({\frac {10\cdot 12\cdot 14\cdot 16}{9\cdot 11\cdot 13\cdot 15}}\right)^{1/8}\cdots.}
  
  Many other series, sequence, continued fraction, and infinite product representations of e have been proved.