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数学 高校生

初めの赤文字の|an-α|<½の、½は、どこから出てきたのでしょうか…。問題のnに-1を入れたのでしょうか? 大学前の予習として独学でやっているので、簡単なことかもしれないですが、教えていただけると助かります💦 回答よろしくお願いします🙇‍♀️

指針 証明方法は e-N論法であるが、 収東しないことを示すから, 更に, 背理法も使う。 キな 18 一第1章 実数と数列 基本 例題014 数列が収束しないことの証明 (e-N論法) 第n項が次の式で表される数列は, 収束しないことを示せ。 (2) 2n 2 ち 数列 a, が実数の定数 αに収束するとして矛盾を導く CHAIRIT ~でないことの証明 背理法が有効 解答(1) an=ー とし、数列 {an} が実数の定数αに収束する 2 と仮定する。 このとき、ある自然数Nが存在し, n>N であるすべての 自然数nについてlan-al< が成り立つ。 Ae-N 論法の適用。 [1] nが偶数のとき a--であるから。-a<より く-く 1 1 2 よって 0<α<1 [2] nが奇数のとき anミー- 2 =であるから。 -の告より よって -1<a<0 0, 2を同時に満たすαは存在しないから, 矛盾である。 よって,数列{an} は収束しない。 (2) an=2n とし, 数列 {an} が実数の定数αに収束すると仮 定する。 このとき,任意の正の実数eに対し, ある自然数Nが存在 し、n>N であるすべての自然数nについて |an-al<e が成り立つ。 すなわち, n2N であるすべての自然数nについて α-e<2n<α+e が成り立つ。 ところが, α+e以上の整数 2n は無数に存在する。これは a+e は有限な 矛盾である。

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英語 高校生

どなたか英語の得意な方この問題問いてくださいませんか、、 先日受験して不安で眠れません

6. 次の英文を読み, 以下の設問に答えよ。 legally as a *trophy. In 2003, a lone hunter killeda rhino on a legal safari in South Africa and brought it back to Asia. Dozens of poachers soon followed. The sound of rifles being fired could be heard in the dark forest just as each paying $50,000 for a hunt. It seems like a lot to pay, but poachers can Damien Mander arrived at his campfire after a long day training *game ranger make as much as $200,000 in profits by selling a pair of horns on *the black recruits in Zimbabwe's Nakavango *game reserve. "There, near the eastern market. boundary," he pointed. He and his rangers grabbed their guns, radios, and ull Many officials in Vietnam are fighting back against reports that the country medical kits. They then drove into the night, hoping to stop the shooter. is the main market for rhino horn, stating that rhino horn bound for Vietnam (21) And so goes a night on the front lines of southern Africa's ruthless * rhino is merely in transit for another country. Do Quang Tung, deputy director of war, which has seen more than a thousand rhinos killed since 2006. At the CITES Managing Authority in Vietnam, said the country "could not be the main bloody heart of this conflict is the rhino's horn, a prized ingredient in traditional market for South African rhino horn," claiming that the majority of Vietnamese Asian medicine. Prices range from $33 to $133 a gram, which at the top end is people would not be able to ( 26 ) rhino horn. Even if there is an emerging double the price of gold. group of people who can ( 26 ) it, he thinks it is too small to make the country Although the range of the two African species 一 the white rhino and its a significant consumer. Professor Dang Huy Huynh, chairman of the Vietnam smaller cousin, the black rhino- has been reduced primarily to southern Africa Zoological Society, says that rhino horn has never been a popular ingredient in and Kenya, their populations had shown signs of improvement. In 2007 white traditional medicine. rhinos numbered 17,470, while blacks had nearly doubled to 4,230 since the mid Recently, there has been a renewed interest in the unproven belief that rhino 90s. horn has healing power. For at least 2,000 years, Asian medicine has prescribed For conservationists these numbers represented a triumph. In the 1970s rhino horn to reduce fever and treat a range of illnesses, but the handful of 22 and '80s, *poaching had nearly caused the two species to become extinct. Ther studies which have been conducted on rhino horn have not found any proof that China banned rhino horn from traditional medicine, and Yemen forbade its ust it can reduce fever. The newest rumor is that it cures cancer, but doctors say in ceremonial knife handles. All signs pointed to better days. But in 2008 th the proof is nonexistent一 no research has been published on the horn's efficacy 23) number of poached rhinos in South Africa shot up to 83, from just 13 in 200' as a cancer treatment. But even if rhino horn is not an effective cure for anything, let alone cancer, that doesn't mean it has no effect, says Mary Hardy. By 2010 the figure had soared to 333, followed by over 400 in 2011. Most of th 27) medical director of Simms/Mann UCLA Center for Integrative Oncology. "Belief horn trade was found to lead to Southeast Asia. in a treatment, especially one that is wildly expensive and hard to get, can have *Javan rhinos once lived in Vietnam's forests. ( 24 ) It had a bullet a powerful effect on how a patient feels," she says. its leg and its horn had been removed. In any event, John Hume believes no rhinos need to die to supply the rhino Even with the rhinos gone, rhino horn can still be found in Vietnam. This 28 25 horn to those who want it. The 69-year-old * entrepreneur has acquired one of because South African law, which complies with the Convention on Internatio the largest privately-owned rhino herds in the world, and currently has more Trade in Endangered Species (CITES), allowS a rhino's horn to be expor ○M3(45)

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