1/1*3+1/3*5+```+1/(2n-1)(2n+1)怎样用裂项法求和?_数学解答

1/1*3+1/3*5+```+1/(2n-1)(2n+1)怎样用裂项法求和?

人气：407 ℃　时间：2020-07-05 12:45:53

解答

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