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数学 高校生

1枚目のan≠0となる証明は理解できたのですが、 2枚目のa1=1>0、an+1=2√an>0より全ての自然数はnに対してan>0であるのはよくわかりません。また、「ーに対してan>0」ってどう言う意味なのでしょう??

基本例題 119 an+1= ST によって定められる数列{an}の一般項を求めよ。 [類 早稲田大〕 基本116 2 an+1= 指針 漸化式 αn+1= an 4an-1 an のように,右辺の分子が α の項だけの場合の解法の手順は panta ① 漸化式の両辺の逆数をとると 答 CHART 漸化式 an+1= an+1= 1=b, とおくと bn+1=p+qbn an an 型の漸化式 bn+1=b+▲の形に帰着。 p.560 基本例題 116と同様にして一般項 bn が求められる。 また,逆数を考えるために, an=0(n≧1) であることを示しておく。 ところが α= panta したがって an ...... ① とする。 SORTIO 4an-1 ① において, an+1=0 とすると α = 0 であるから, an=0 とな るnがあると仮定すると an-1=an-2==q=0 an= 1 a₁=²/²/² ( (0) であるから,これは矛盾。 よって,すべての自然数nについて αn≠0 である。 ① の両辺の逆数をとると 1 an+1 an 両辺の逆数をとる panto 1 bn 9 -=-= an an+1 =4- bn+1=4-bn an bn+1-2=-(bn-2) 1 = b とおくと an これを変形すると また 1-2=5-2=3 b1-2=- a1 ゆえに,数列{bn-2} は初項 3,公比 -1 の等比数列で bn-2=3.(-1) すなわち bn=3・(-1)"'+2 1 3.(-1)"¹+2 19 00000 Egon an=05 an-1=0 これから an-2=0 以後これを繰り返す。 33d= 逆数をとるための十分条件。 1 an+1 THO Jia Il si ◄bn= 4an-1 an 特性方程式 α =4-α から α=2 an bn=0 という式の形から 565 3章 15 漸化式と数列 で , n). き き q 数 c)dx )に

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英語 高校生

Aの1,2,3はこれで合ってますか? 間違えていたら教えて下さい🙇‍♀️

2 Grammar Future with will, may, and might) 4.23 You can use will to give facts or predictions about the future. adol Looking ahead UNIT 12 Extra practice p. 151 To show you are not 100% sure about the future, you can use may and might. I'll be 65 in June. It'll be expensive to travel around Europe. The baby will keep us busy! It won't be easy to find a job. I'll = / will won't = will not I may go on for a master's degree. I might not be able to afford it. You can also use will with expressions like I guess, I think, maybe, and probably. We'll probably take some time off from work. Maybe we'll move to Arizona. Avoid will to talk about plans or decisions already made. Use the present continuous or be going to. I'm going to Europe next year. I'm going to visit Paris. (NOT I will go to Europe next year. I will visit Paris.) Common errors A Circle the correct options in the conversations below. Compare and practice in groups of three. 1. A What are you going to do at the end of this course? B. I'm not sure. I guess I take /I'll take another course. C I don't know. I'm going to / I may travel abroad with my brother. He thinks his classes might / can finish early this year, so we might / will be able to go in May. Don't use can for predictions. Use may or might. I may go away for vacation. (NOT I can go away for vacation.) 2. A Are your friends going away for vacation next summer? B Well, they're all going to do / will all do different things. One friend is going / will go to Istanbul. I'd love to go, too, but I don't know. I won't / I might not be able to afford it. C Four of my friends will / may be 21, so we're having have a big party. It's going to be fun. 3. A Are you going to look for a new job next year? B Actually, I just got a new job. I'll / I'm going to work for the local newspaper. How about you? C I don't know. I think I'm studying / I'll study for a certificate in nutrition. I mean, I'll / I may probably go back to school because I'm pretty sure I won't / might not get a job. Give your own answers. Who has interesting plans?

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