20.？ (Full score of this question 13) There are two questions in this question * * *? Small questions, 5 points for the first small question and 8 points for the second small question.

Known sequence? What is the sum of the preceding paragraphs? And then what? ,?

(1) Proof:? Is a geometric series;

(2) looking for a sequence? Find out what the value of n is. Find the minimum value and explain the reason.

(2)? =? N= 15 gets the minimum value.

Analysis: (1)? When n? When 1, a114; When n≥2, an? Sn？ Sn？ 15an？ 5an？ 1? 1, so? ,

A 1 again? 1 15≠0, so the series {an? 1} is a geometric series;

(2)? By ( 1):？ , too? , from this? (n？ n *)；

Solving inequality sequence number

Similarly, when n≤ 15, the sequence {Sn} decreases monotonically; So when n? At 15, Sn reaches the minimum value.

See the figure below for details: