...{an}的前n项之积,满足Tn=1-an(n∈N*).(1)设bn=1Tn,证明数列{bn}是...

（1）∵Tn=1-an（n∈N*）．an＝TnTn?1(n≥2)，∴Tn＝1? TnTn?1，∴1＝ 1Tn?1Tn?1(n≥2)
∵bn＝1Tn，∴bn-bn-1=1，∵Tn=1-an，∴T1＝12，∴b1＝1T1＝2，∴数列{bn}是以2为首项，以1为公差的等差数列，∴bn=n+1，∴Tn＝1n+1，∴an＝1?1n+1
（2）Sn=T12+T22+…+Tn2=122+132+…+1(n+1)2＞12×3+13×4…+  1(n+1)(n+2)＝12?1n+2＝an+1?12
∴an+1?12＜Sn
当n≥2时，=122+132+…+1(n+1)2＜122+已赞过已踩过你对这个回答的评价是？评论收起 ._1uevpeq{zoom:1;background-color:#fff;border:0;margin-bottom:10px;padding:30px 0 20px 42px;position:relative}._1uevpeq.ec-1841{padding:20px 0}._1uevpeq.ec-2246{padding:20px 0 10px}.ec-1841 .y7we4hu{font-size:16px;margin-bottom:-5px}.y7we4hu{color:#7a8f9a;height:25px;line-height:25px;overflow:hidden;position:relative}.y7we4hu h2{margin:0;padding:0}.y7we4hu:after{clear:both;content:" ";display:block;height:0;visibility:hidden}a.tycfu7u{color:#666;float:right;font-size:12px;margin-left:8px;text-decoration:none}.hhhv6ex{color:#666;font-size:13px;line-height:normal;line-height:20px;margin-top:10px}.vnsdjzp{margin-top:15px;position:relative}.vnsdjzp h3{font-weight:400;padding:0}.vnsdjzp a{text-decoration:none}.vnsdjzp em{color:#d81419;font-style:normal}.ec-2246 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