Sn为数列{Bn}前n项的和Bn=1/(4n(n+2))求证Sn永远小于3/16_数学解答

Sn为数列{Bn}前n项的和
Bn=1/(4n(n+2))
求证Sn永远小于3/16

人气：485 ℃　时间：2020-04-16 15:34:14

解答

Bn=1/[4n(n+2)]=[(1/n-1/(n+2)]/8
Sn=[(1-1/3)+(1/2-1/4)+……+(1/n-1/(n+2))]/8
=[1+1/2-1/(n+1)-1/(n+2)]/8