计算1/1*3+1/3*5+1/5*7+...+1/(2n-3)(2n-1)+1/(2n-1)(2n+1)_数学解答

计算1/1*3+1/3*5+1/5*7+...+1/(2n-3)(2n-1)+1/(2n-1)(2n+1)

人气：465 ℃　时间：2020-01-28 12:02:46

解答

=1/2(1-1/3+1/3-1/5+1/5-1/7+……1/(2n-3)-1/(2n-1)+1/(2n-1)-1/(2n+1))
=1/2(1-1/(2n+1))
=1/2-1/(4n+2)