數學: 簡化2

0/1! - 1/2! + 2/3! - 3/4! + 4/5! - ...
= (1 - 1)/1! - (2 - 1)/2! + (3 - 1)/3! - (4 - 1)/4! + (5 - 1)/5! - ...
= (1/1! - 1/1!) - (2/2! - 1/2!) + (3/3! - 1/3!) - (4/4! - 1/4!) + (5/5! - 1/5!) - ...
= (1/1! - 1/1!) - (1/1! - 1/2!) + (1/2! - 1/3!) - (1/3! - 1/4!) + (1/4! - 1/5!) - ...
= 1/1! - 2/1! + 2/2! - 2/3! + 2/4! - 2/5! + ...
= 1 + 2(-1/1! + 1/2! - 1/3! + 1/4! - 1/5! + ...)
= 1 + 2(- 1 + 1 -1/1! + 1/2! - 1/3! + 1/4! - 1/5! + ...)
= 1 + 2(- 1 + e⁻¹)
= 2e⁻¹ - 1

2011-10-17 00:41:21 補充：
不管打漏字是無心或有意,得到回答後才換題不太好吧...

Sorry, 打漏了個2字,分母應該是(2n+1)!