(1)证明:∵anan+1=( 1 2 )n,∴ an+2 an = 1 2 ,∴数列a1,a3,…a2n-1,是以1为首项, 1 2 为公比的等比数列;数列a2,a4,…,a2n,是以 1 2 为首项, 1 2 为公比的等比数列.(2)解:T2n=(a1+a3+…+a2n-1)+(a2+a4+…+a2n)= 1? 1 2n 1? 1 2 + 1 2 (1? 1 2n ) 1? 1 2 =3(1- 1 2n ).