1番上の式で、このような式の場合両辺をn(n+1)で割るというのは決まっているんですか？ それとも自分で思いつくしかないのでしょうか、、

(2) nan+1=(n+1)am+1 の両辺を n(n+1) で割 ると an+1 an 1 三 n+1 n 1 とおくとb+1=bn+ an bn 三 n b、=4=2 また 1 よって, 数列 (b,}は初項が2, 階差数列の第1 項が n(1n+1) 1 であるから, nN2のとき Ses も。-2+三E-24 点) 1 =2+2 k=1\e n-1 1 k=1 k(k+1) k+1 1\ 3 2 1 n-1 n 3n-1 =2+(1 …D n n

chemicalとchemistryの違いは何ですか。

英語教師も迷っていたところです。 代名詞thatが24の文末にあるのですが これはchemicals のことをいうのか raw materialsのことをいうのか？ 皆さんの意見お聞きしたいです！

CIothes. 7 (2t can take/more than 20,000 liters of water to pr 有等である kilogram of cotton, / equivalent to/a single T-shirt and a pair of jeans. ! (24)Up to S 生の原材料 8,000 different chemicals are used / toturnraw materials into clothes」/ so we must 処分する方法 O Consider how to dispose lof them. // (25)If we do not do it properly, / these chemicals

訳を教えてください！！

Have you ever heard the saying, "Laughter js cheerful, best medicine"? It means that 1f we are We we can keep ourselves healthy. Usually, when laughter is als0 good for our health. Recent studies show the following facts: 1) The body produces several kinds of chemicals when we laugh. 2) Some of these chemicals are natural painkillers. Now, some doctors and nurses are trying to use laughter as a new medical treatment. One of the doctors introducing this idea is Madan Kataria. He started "Laughter Yoga" in India in the late 1990s. 聞いて、最も適切な答えを選びましょう。 English, and choose the row

教えてほしいです！！お願いします！！

問題は【1】~【4】まである。答えは各問題の指示に従って別紙の解答用紙に書きなさい。 【1】次の英文を読んで設問に答えなさい。 Headaches are a big problem. Each year, millions of people suffer from severe headaches that affect their enjoyment of life, (1) not to mention their productivity at work. estimate, headaches cost individuals and businesses more than (2) $50 billion each year! (3) This is one of the reasons research into headaches has become a worldwide effort. Although he did not know much about how headaches work, Hippocrates was the first doctor to find a way to treat them. By 400 BC, Hippocrates had discovered that the *bark from willow trees was useful in treating pain. He made a white powder from the tree's bark and gave it to his patients. Hippocrates did not know it, but he was actually prescribing a natural chemical in willow bark called salicin. Whena person eats salicin, the chemical is changed inside his or her body into (4) salicylic acid. It turns out that salicylic acid is good for stopping pain, including headache pain, but it is bad for a person's stomach. In the 1800s, a chemist in Germany slightly changed easier for people to take. commonly known as aspirin. Aspirin was used throughout most of the 1900s to treat headaches, but doctors had little idea about what really caused headaches. When doctors can *diagnose the cause of a disease, they can find better ways to treat it. Therefore, as medical technology developed, doctors began to use it to learn more about the human brain and about headaches. In fact, according to one m to make it This new form of the chemical was called acetylsalicylic acid, now acid's Now doctors classify headaches ( A ) two general types: primary and secondary. A primary headache is a condition ( B) as only the headache itself. one caused by another physiological condition, such as an *infection or a *tumor. For primary headaches, doctors have determined three possible causes. headache is caused by stress. characteristically felt on both sides of the head as a dull, steady pain. Another kind of primary headache is the *migraine headache. Exactly what causes these headaches is not well understood, but many experts believe it could be abnormal brain activity causing changes in the brain's chemistry and blood flow. For many people, migraines are caused by certain (5) stimuli, such as poor sleep or particular foods or smells. A sufferer usually feels intense pain on one side of the head and becomes sensitive to light and noise. If the migraine is severe, the sufferer may *vomit repeatedly. The third kind of primary headache is known as the cluster headache. Cluster headaches typically occur around the same time each day for weeks or months at a time. The person ( C)from this kind of headache usually feels pain on one side of her or his head, and the pain is centered around one of the eyes. Doctors do not know much (6) at present about cluster headaches, but they seem to be more common among men and could be related to alcohol or other things that affect a person's blood flow. Using computers and more advanced medical equipment, doctors continue to learn more about what happens in the brain before and during headaches. Especially in the case of migraines, some doctors believe they have found the part of the brain that sets off the reaction for severe attacks. With these insights into brain processes, doctors hope new ways will be discovered to stop headaches before they begin. On the other hand, a secondary headache is One kind of primary Doctors usually call these tension headaches, and they are 注: bark 樹皮 diagnose ~を診断する、~を突き止める 感染症·伝染病 migraine (headache) 偏頭痛 infection tumor 腫場 vomit 食べたものを吐く (出典:READING FOR THE REAL WORLD 3rd edition, Compass Publishing より)

なぜEにはmuchが入るのでしょうか smallを入れてしまいました

(C)we use sound and sight, they depend primarily on pheromones", chemicals secreted" by individuals and smelled or tasted by nestmates. ( D) the brain of an ant weighs less than one- millionth as (E ) as a human brain, it is not surprising that a given species produces just ten to twenty signals. Unlike human language, these messages are entirely instinctual. These marvelous little creatures have been on Earth for more than 140 million years. The most

3の(2)が分かりません。 教えていただきたいです。 またその他あっていますでしょうか？ よろしくお願い致します。

下線部に注意して、各組の英文を日本語に直しなさい。 3 ロ1(1) I regret not saying goodbye to her. 板女に十を行げなかったことを使悔してる 2セは不当だく言われていて微花です データを解することをを十ないで下さい。 データを格したことをはっぜソと覚えています. 彼は別の葉oと通加しょうとしなした。 Isnid D (2) I regret to say that the rumor is true. 口2(1) Please remember to save the data. (2) I clearly remember saving the data. 口3(1) She tried to add another chemical. (2) She tried adding another chemical. *chemical: 薬品

文構造はあってますか？ また、1つ目のthatは何を表していますか？

The idea is thaf chemicals<lthatl are releasedd by the car driving down the roads) 出される ~にさって will be absored by the leaves of trees above them. ヘによって その考え方は、適路を走っている車によって排出されると学物質は頭上の木の業によって 『及収されるだろう、というものである。

「化学のレポート」を英語にするときに解答で chemistry paperとなっていたのですがchemical paperでは間違いですか？間違っていたら、その理由も教えてください。 よろしくお願いします！

Power on 2のLesson 6です！写真が本文なのですが、Part 3にはいくつの長所が書かれてますか？

Tas Lesson6 Vegetable Factories 予習プリント PAF Task-1: Translate underlined parts into Japanese C C PART 1 Takumi: Angelina, have you ever heard of vegetable factories? I learned about them for the first time on TV last night. Such factories were first built in Denmark in 1957, and similar factories were PAI also introduced in the US in the 1970s. Angelina: Vegetable factories-yes, 1 know about them, too. In Japan, they were first built in the early 1980s to produce kaiware sprouts. These factories are now attracting much attention as a new type of agriculture I hear new vegetables like frilice lettuce and ice plant are being produced there. Takumi: Wow! You really knowa lot about vegetable factories. Angelina: Would you like to know more? Takumi: Definitely! もちろみ に C フリルレタズ C PA C C C PART 2 C You may be surprised to hear that we can grow vegetables without the sun and soil. But that is what people do in vegetable factories. In these factories, electric light and fertilized water are used instead of the sun and soil. Temperature and humidity are also controlled. It seems that limited space in vegetable factories is not a big problem. Workers fully use the space by stacking shelves of vegetables. Actually, you can find small vegetable factories in the previolisly wasted space of office buildings or restaurants. At present, the main crops from vegetable factories are leaf vegetables. But in the near future, PA C C Ta more varieties of vegetables are sure to come. し]必ず…する PART 3 What are the good points of vegetable factories compared to traditional agriculture? For one thing, they can provide a stable supply of vegetables, even in bad weather conditions. For another thing, vegetables grow much faster in a controlled environment. Other good points include no use of chemicals and good taste with more vitamins. Unfortunately, vegetable factories still face one challenge. Running them requires a lot of money. Because of this cost, these vegetables are expensive to buy. Hopefully, in the near future, we will have solved this problem. うまくいけば PART 4 文に、科に Talkumi: Agriculture without the sun and soil. Hmm. That's a great idea indeed. Honestly, Ive got a bit of, ahem, “agriculture shock" from what you've just told me in a good way though. Angelina: Ha-hal Have you? Good. If we can develop vegetable factories on a large scale, we may be able to solve the problem of food shortages. Takumi: Yeah, I agree. And the way we view vegetables may change whether we like it or not. Oh, by the way, Angelina, culture and agriculture are closely related, as you can see from the words. Agri-means “farming," and culture means “to grow something." Angelina: Oh, so you're giving alecture now! 422words