Question

已知数列an中，a1=1,an+1=an/(an+3)(n∈N*) 求证:数列｛1/an+1/2｝

已知数列an中，a1=1,an+1=an/(an+3)(n∈N*) 求证:数列｛1/an+1/2｝是等比数列，并求an的通向公式

Answer 1

是an+3还是a(n+3)还有an+1也是

追问

a(n+1) (an)+3

追答

求证:数列｛1/an+1/2｝是等比数列，即(1/a(n+1)+1/2)/(1/an+1/2)=k,

a1=1,an+1=an/(an+3)=>1/(a(n+1)=3((1/an)+1/3)

=>1/(a(n+1)=3((1/an)+1/2)-1/2
=>(1/a(n+1)+1/2)/(1/an+1/2)=3成立
且1/an+1/2=0.5*3^n
an=1/(0.5*3^n-0.5)

Answer 2

将汇聚轰轰ihihouijoj