已知an=1/（2^n－1）若数列bn满足bn=2^n an a（n+1）,Sn＝b1+b2+b3+……bn,求证Sna1=1_数学解答

已知an=1/（2^n－1）若数列bn满足bn=2^n an a（n+1）,Sn＝b1+b2+b3+……bn,求证Sn
a1=1

人气：255 ℃　时间：2020-05-16 13:51:32

解答

bn = 2^n.an.a(n+1)
= 2^n/[(2^n-1)(2^(n+1) -1)]
= 1/(2^n-1) -1/(2^(n+1) -1)
Sn=b1+b2+...+bn
= 1/(2-1) - 1/(2^(n+1) -1)
= 1- 1/(2^(n+1) -1)
Sn < 1 好像是这样