Question

已知数列a1=1,an*a(n+1)=(1/2)^n.1,求证数列{a2n}与{a(2n-1)}n?N*都是等比数列.求

Answer 1

an*a(n+1)=(1/2)^n.

a(n+1)*a(n+2)=(1/2)^(n+1)

2式除以1式得

a(n+2)/an=2

数列{a2n}与{a(2n-1)}n?N*都是等比数

T2n =S奇+S偶

=(1+2+4+ … )+(2+4+8+… ) 每个括号内都有n项

=3(1-2^n)/(1-2)

=3*2^n-3