數學:化簡(2.1)

用戶9112

2011-10-17 3:03 pm

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

圖片參考：http://i1090.photobucket.com/albums/i376/Nelson_Yu/int-109.jpg

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

回答 (1)

用戶2053

2011-10-17 9:29 pm

✔ 最佳答案

∞
Σ (-1)ⁿ n / (2n+1)!
n=0
= 0/1! - 1/3! + 2/5! - 3/7! + 4/9! - 5/11! + 6/13! - 7/15! + ......
= ( (1 - 1)/1! - (3 - 1)/3! + (5 - 1)/5! - (7 - 1)/7! + (9 - 1)/9! - (11 - 1)/11!
+ (13 - 1)/13! - (15 - 1)/15! + ...... ) / 2
= ( 1/1! - 1/1! - 3/3! + 1/3! + 5/5! - 1/5! - 7/7! + 1/7! + 9/9! - 1/9!
- 11/11! + 1/11! + 13/13! - 1/13! - 15/15! + 1/15! + ......) / 2
= ( 1/1! - 1/1! - 1/2! + 1/3! + 1/4! - 1/5! - 1/6! + 1/7! + 1/8! - 1/9!
- 1/10! + 1/11! + 1/12! - 1/13! - 1/14! + 1/15! + ......) / 2
= (( 1 - 1/2! + 1/4! - 1/6! + 1/8! - 1/10! + 1/12! - 1/14! + ... )
- ( 1 - 1/3! + 1/5! - 1/7! + 1/9! - 1/11! + 1/13! - 1/15! + ... )) / 2
= ( cos 1 - sin 1 ) / 2

👍 0 👎 0