由g(xn?1)?∴xn?1?2?1f(xn)(n?N*)得:xn?1??cosxn, n2n?2??11?1?cosxn?sin(xn?)??xn? (n?N*) ??????8分 nn2n2∴xn??2?1???1??xn?1?,xn?1???xn?2?,??,x2??x1?,
2n?2222n?12?1????, ????????????????10分
(n?1)!2从而xn??2x1??2?x2??2?x3???2???xn?1?11?1???1111???????????? ?11分 2?1!1!2!3!n!?21? ??1?1??2???n?1????
222?2? ??1?2(1?n)??????3?n?1???? ???????13分 222???2? ?3?????1???1?????5????(???,?) 2?66????xn?1?∴x1??2?x2??2?x3??2?2??(n?N*)成立。 ???????14分
高三理科数学试题第 11 页(共7页)