an的通项公式为an=2n-1数列bn=1/(anan+1)其前n项和Sn等于_数学解答

an的通项公式为an=2n-1数列bn=1/(anan+1)其前n项和Sn等于

人气：280 ℃　时间：2019-10-29 21:57:18

解答

bn=1/(2n-1)(2n+1)
=1/2*2/(2n-1)(2n+1)
=1/2*[(2n+1)-(2n-1)]/(2n-1)(2n+1)
=1/2*[(2n+1)/(2n-1)(2n+1)-(2n-1)/(2n-1)(2n+1)]
=1/2[1/(2n-1)-1/(2n+1)]
所以Sn=1/2*[1/1-1/3+1/3-1/5+……+1/(2n-1)-1/(2n+1)]
=1/2[1-1/(2n+1)]
=n/(2n+1)