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数学 高校生

問題⑵⑶の数学的帰納法について4つ質問させて下さい!質問量が多くてすみません… ①写真1枚目の赤の下線を引いた部分について、私の解答(写真2枚目)では全て、整数でなく自然数と書きました。私は赤線部分は自然数の範囲に収まるのかなと思っていたので、なぜわざわざ整数と書いている... 続きを読む

2021年度 〔4〕 α=2, b=1および リー an+1=2a+36, b +1=α+2b (n=1, 2, 3, ...) で定められた数列{an}, {bn}がある。 C = a b とおく。 (1) c2 を求めよ。 149 (2) cm は偶数であることを示せ。 (3) nが偶数のとき, cm は28で割り切れることを示せ。 ポイント 連立の漸化式で定められる2つの数列の一般項の積についての数学的帰納法 による証明の問題。 (1) 漸化式でn=1 とおいて求める。 (2) 数学的帰納法により証明する。 (3)n=2mとおいて, m について数学的帰納法で証明する。 解法 (1) a2=2a+3b1=4+3=7 b2=α +261=2+2=4 より C2=azbz=7×4=28 (2) a1=2,b=1,4+1=2a+3bb1=an+2b (n=1, 2, 3, ... より帰納的に a b が整数であると言えるので, cm=amb" も整数である。 cm が偶数であることを数学的帰納法により証明する。 (I)n=1のとき,c=a,b=2×1=2より C1 は偶数である。 (II)n=kのとき cが偶数であると仮定すると, a b は偶数であるから=211は 整数) とおける。 n=k+1のとき ( Level A TRAIGHT Ck+1=ax+1bk+1=(2a+3b) (+26) =2a²+7ab+6b²=2a²+14Z+6b2² =2(a²+71+3b²2 ) ここで, a2+71 + 3b²2 は整数であるから Ck+1 も偶数である。 (I), (II)より すべての自然数nに対してcm は偶数である。 (証明紋) (3) n=2m(mは自然数とおき, C2mm が28で割り切れることを数学的帰納法によ り証明する。 (I) m=1のとき, c2 = 28 より 28で割り切れる。 (II) m=kのときc2が28で割り切れると仮定すると, 28 (1は整数)とおけ る。 m=k+1のとき C24+2=a2+2b24+2 = (2a2+1+3b2+1) (a2+1+2b2+1) = {2 (2a2+362) +3 (a₂+2b₂)}{2a+3b₂+2 (a₂+2b2x)} = (7a2 + 12b2) (4a24+7b₂24) = 28a2²+97a2b2+84b2² = 28a2²+97-28/+84b2x² = 28 (a24² +971 +3b₂²) D ここで, a² +971 +3bz² は整数であるから 22は28で割り切れる。 (I), (II)より. すべての自然数mに対して C2me は28で割り切れる。 ゆえに,nが偶数のとき, cm は28で割り切れる。 (証明終)

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英語 高校生

至急!!私立大学看護学部の過去問です。答えがないため、回答を作って欲しいです!!科目は英語です。

問題番号に対応 効とする。 うち受験票お researchers at the University of Veterinary Medicine in Vienna, Austria, have found. Dogs won't give food to a human, even if that person gave them some food first, and that they would help other dogs that had helped them before. Therefore, the team Previous studies have shown that dogs can recognize cooperative and uncooperative humans, "reciprocal altruism"- that is, doing a good thing in return to a human who had given expected to find that their test subjects would put these two things together and show To start, the team trained a group of 37 dogs to press a button which would activate a them food first. *enclosure with the dispenser, while one of (2) two humans was in a separate enclosure with the button. One would press the button to food dispenser. Then, they put each dog in an would not. Each dog was paired with both humans in give food to the dog, and (4) unhelpful one. turn. After that, the researchers switched over the button and the dispenser. They expected that the dogs would press the button to give food to the helpful human but not to the though the dogs did press the button, they did it just as often when either human had the food dispenser, and even when no human was there at all. "In these kinds of studies (5) [perform / to / dogs / which/ trained / are in a particular behavior for an experiment, they will usually do the behavior a few times as they have simply learned the association between the behavior and getting a reward, and it may be enjoyable for them to do the behavior," said Jim McGetrick, a PhD student at the University of Veterinary Medicine in Vienna who led the research. 身を正しく が本冊子 1番 2 次の英文を読んで下の設問に答えなさい。 (3) giving us some food? Are they a combination of reasons. "It is (6) Why wouldn't our best pals want to help us out by secretly all bad boys and girls? McGetrick believes there is possible that the dogs did not understand enough about the task to realize that only one of the humans was providing them with food," he said. It could also be because they didn't fully understand the button and dispenser system, or because they were too focused on the food to notice whether a particular human was pressing the button or not. "Having said all that, even if they did completely understand the task and were fully attentive to the actions of the humans, there is still a good possibility that they wouldn't have given food back in return," he added. "It could be that providing food to a dog as they do not typically do that in everyday life." After all, humans are the ones who human is something very strange for (7) already have food, from a dog's perspective. why would your pet need to worry about (8) making sure you have enough? However, all the humans in the study were people the dogs didn't know. "It is quite 5

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英語 高校生

至急!!私立大学看護学部の過去問です。答えがないため、回答を作って欲しいです!!科目は英語です。

プペンシルで解 people than ever can find an audience time filled with disasters, online, "conspiracy theories seem to be growing crazier by the day. We also tend to believe in such things under increased stress, which is unfortunate because many of these ideas are Some conspiracy theorists pride themselves on being "critical freethinkers," but a new damaging our democracies and ourselves. study showing a connection between lower critical thinking skills and increased conspiracy (2) theory belief suggests this may not be the case. "Conspiracy theories refer to attempts to explain the ultimate cause of an important event (social, political, climatic, etc.) by accusing a hidden group of perceived evil, powerful people or organizations of having secretly planned and carried out these events," say Paris Nanterre University psychologist Anthony Lantian and team in their paper. two studies, the researchers tested the critical thinking skills of 338 a French version of the Ennis-Weir Critical Thinking Essay Test. They then scored the students' tendencies towards conspiracy beliefs and their personal Across undergraduate students (4) the objective analysis and assessment of their own critical thinking skills. Critical thinking. evaluation of a situation requires a collection of cognitive skills. These include the ability to distinguish between relevant versus irrelevant information, think systematically, see other perspectives, recognize and avoid logical *fallacies, look beyond the obvious, be aware of and avoid biases, and change your mind in light of new evidence. "The more people believe in conspiracy theories, the worse they perform on a critical thinking ability test," Lantian said. "This test is characterized by an *open-ended format highlighting several areas of critical thinking ability in the context of argumentation." (6) All this is not to say that those with high critical thinking skills can't also be sucked into believing things that may not necessarily be true. The way (7) [is wired /a/ makes / thinking/ social species / our / as] us very vulnerable to believing those we identify with as part of our own cultural group- no matter how much education we have had that boosts science literacy. Trust plays a massive role in who we believe. We also have a tendency to believe each of us is above average at detecting misinformation, which can't possibly be true. Researchers have also linked this need to feel special to greater belief in conspiracies. Lantian and team point out that while their study suggests critical thinking lowers Deople's chances of believing in untrue conspiracy theories, the findings don't determine if (8) (9) た場合,そ 数学【数学 験番号 【化学 b てお 3 In a more (1) ① 次の英文を読んで、下の設問に答えなさい。 1 - (3) the po no a E

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