高一数学题【帮忙看一下 要过程 谢谢了】

数列bn=log2(an-1) (n属于N*)为等差数列,→
an-1为等比数列
且a1=3,a3=9 →b1=log2(3-1)=1,b3=log2(9-1)=3,
∴b2=2,→log2(a2-1)=2→
a2-1=4,a2=5∴{an}={3,5,9,......}
∴{an-1}={2,4,8,......}为等比数列

证明:1/(a2-a1)+1/(a3-a2)+……+1/(an+1-an)=
1/(5-3)+1/(9-5)+……+1/(2^(n+1)-2^n)=
1/2+1/4+……+1/2^n=(等比数列)
(1/2)[(1-(1/2)^n]/(1-1/2)=[(1-(1/2)^n]