1, Solution: (1) Change the condition to: 1-=, so {1-} is a geometric series, and its first term is

1-, the common ratio, so 1-=, so an = (n? 1)………… 1

(2) Certificate: press 1, a 1? a2？ …an=

As evidence, a 1? a2？ ..... Ann<2? n！

Just prove that n? There are ...............................................................................................................................................................................

Obviously, every factor on the left is a positive number. Prove it first. For every n? N* yes

1-()…………3

Prove three formulas by mathematical induction;

(i) When n = 1, the 3-equation is clearly established.

(ii) When n = k, Equation 3 holds,

Namely. 1-()

Then when n = k+ 1,

〔 1-()〕? ()

= 1-()-()

1- () That is, when n = k+ 1, the cubic equation also holds.

So for everything, n? The formula N*, 3 holds.

Get it with 3. 1-()= 1-

= 1-= >

So equation 2 holds, and the conclusion holds.