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English Senior High

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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Mathematics Senior High

解答一行目について、S2n-1なのに数列の最後の分数の分母が2n-1ではなくnであるのはなぜですか?

有限の から第頂ま r1のとき 1-r 比級数 Zon は 確認して 基本 例題 125 2通りの部分和 S2n-16 S2 の利用 .......... (1) 級数 ① の初項から第n項までの部分和をS" とするとき, San-1, Sam をそれ ぞれ求めよ。 (2) 級数①の収束、発散を調べ、収束すればその和を求めよ。 12/11/12/11/11/11/1①について + + + 3 3 4 4 無限級数 1 -- 指針 (1) S2- が求めやすい。 S2 は S2=S2n-1+ (第2 項) として求める。 (2) 前ページの基本例題124と異なり、ここでは( )がついていないことに注意。 このようなタイプのものでは, Smを1通りに表すことが困難で, (1) のように, S-1 S2 の場合に分けて調べる。 ......... そして、次のことを利用する。 (1) S21=1- [1] lim S2n-1 = lim S2 = S ならば limS=S 22-00 11 00 {S} は発散 San S2n-1- [2] lim S27-1≠lim San ならば 12-00 1 2 2 -1-(1/2-1/21)-(1/13-1/1)- + 1 1 1 1 1 + + 3 3 4 4 3)-.. Sp-Sn-1-1-1-1 =1- 748 limSn=1 - lim S27-1=1, limS2"=lim(1- 00 上の例題の無限級数の第n項を (2) (1) から よって 72-00 したがって, 無限級数 ① は収束して, その和は1 21-00 検討 無限級数の扱いに関する注意点 3 3 + 2 2 71-00 1 n (1-₁)= n+1 1 1 -=+= 22 n n 1 1 (1) ++++++ 3 2 22 3² 2333 (2) 2- 4 4 ・+ 3 3 =1+ 練習 次の無限級数の収束 発散を調べ, 収束すればその和を求めよ。 125 1 1 1 1 +...... JEDNU 1 1 と考えてはいけない。 ( )が付いている場合は,n n n+1 番目の( )を第n項としてよいが,( )が付いていない場合は, n番目の数が第n項となる。 注意 無限級数では、勝手に( )でくくったり、項の順序を変えてはならない! [例えば, S=1-1+1−1+11+ ·····=(1-1)+(1-1)+(1-1)+...... とみて, S = 0 などと] したら大間違い! (Sは公比-1の無限等比級数のため、発散する。) S=02221 などと ただし, 有限個の和については,このような制限はない。 __n+1 + |基本 124 部分和 (有限個の和)なら ( )でくくってよい。 [参考] 無限級数が収束すれば, その級数を、順序を変えずに 任意に( )でくくった無限級 数は,もとの級数と同じ和に 収束することが知られている。 n+1n+2 n n 211 n+1 (p.217 EX94 4章 15 無限級数 2

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