题目

已知a、b均为正实数，n∈N*，求证：(an＋bn)≤(an+1＋bn+1). 答案：证明：(an＋bn)－(an+1＋bn+1)＝［(an＋bn)(a＋b)－2(an+1＋bn+1)］＝(abn＋anb－an+1－bn+1)＝［a(bn－an)＋b(an－bn)］＝(bn－an)(a－b).∵a、b为正实数，n∈N*，∴a＋b＞0，a－b与an－bn同为正或同为负或同为零.∴·(bn－an)(a－b)≤0，即≤(an＋1＋bn＋1).I found out one time that doing a favor for someone could get you into a lot of trouble. I  was  36   the eighth grade at the time, and we were having a final    37  . During the test，the girl  38   next to me whispered something，but I didn’t understand. So I leaned(倾斜) over her way and found out that she was trying to ask me  39 I had an extra pen. She showed me that  40  was out of ink and would not write．I happened to have an extra one，so I took it out of my pocket and put it on her desk．Later, after the test papers had been  41 the teacher asked me to  42  in the room when all the other students  43   . As soon as we were alone, she began to talk to me about  44  it meant to grow up；she mentioned how important it was to stand  45   your own two feet and be responsible for your own acts. For a long time, she talked about __46 _and emphasized the fact   that when people do something dishonest，they really  47  themselves．She made me promise that I would think  48   about all the things she had said. Then she told me I could   49  . I walked out of the room wondering   40   she had chosen to talk to me about all those things． Later on，I found out that she thought I had cheated on the test. When she saw me lean over to talk to the gir1 next to me, it looked   51  I was copying answers  52   the girl’s test paper. So I came to find her and tried to explain about the pen, but all she could say was it seemed very strange to her that I hadn’t   53   anything about the pen the day she talked to me right after the test.  54   I tried to explain that I was just doing the girl a favor   55  letting her use my pen, I was sure she continued to believe that I had cheated on the test．【小题1】A．fromB．onC．inD．at【小题2】A．lessonB．testC．classD．papers【小题3】A．seatB．seatingC．sittingD．sit【小题4】A．whetherB．whyC．whereD．that【小题5】A．oneB．thatC．itD．hers【小题6】A．handedB．turned inC．given outD．marked【小题7】A．workB．readC．stayD．study【小题8】A．gone outB．were studying C．were thereD．were dismissed【小题9】A．howB．whyC．whatD．which【小题10】A．byB．onC．toD．with【小题11】A．honestyB．faithC．confidenceD．reliability【小题12】A．improveB．punishC．cheatD．help【小题13】A．wellB．highlyC．honestlyD．seriously【小题14】A．leaveB．go onC．sit downD．refuse【小题15】A．ifB．whetherC．whyD．how【小题16】A．likeB．as thoughC．asD．that【小题17】A．forB．byC．fromD．at【小题18】A．mentionedB．askedC．answeredD．realized【小题19】A．Long beforeB．As long asC．Just asD．Even though【小题20】A．withB．byC．inD．through