我们知道,对于无穷递缩等比数列{a_n}(a_n=a_1q~(n-1),0<|q|<1),有S=a_1+a_1q+a_1q~2+…+a_1q~(n+1)+…=a_1/1-q笔者发现,有不少证明数列不等式的高考题若逆用此公式来证,将变得非常简洁自然.例1(2002年高考全国卷理科第22题第(2)小题)设数列{a_n}满足a_(n+1)=a_n~2-na_n+1(n∈N~*).当a_1≥3,n∈N~*时,证明: We know that there is S = a_1 + a_1q + a_1q ~ 2 + ... + a_1q ~ (n) for infinitely contractible geometric progression {a_n} (a_n = a_1q ~ (n-1) +1) + ... = a_1 / 1-q The author found that there are many proof of the inequalities of the college entrance examination questions if the reverse use of this formula to prove, will become very simple and natural. (2)) Suppose the sequence {a_n} satisfies a_ (n + 1) = a_n ~ 2-na_n + 1 (n∈N ~ *). When a_1≥3 and n∈N ~ *