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TOEIC・English Undergraduate

わからないので答えを教えてもらいたいです。

英語 Amy: Hey Jake, I was thinking about online shopping this weekend. Do you shop online often? Jake: Yeah, I do it quite a bit. It's so ( house and you can ( ) almost anything online. That's true. I love the convenience, too, especially with a busy schedule. But I've heard there are some downsides to it. What do you think? Well, one obvious downside is not being able to ( ) or try the product before buying. Sometimes, what you see on the website isn't exactly what you get. Amy: Yeah, that's a good point. I've had a couple of instances where the color or size was ) from what I expected. ( Another thing is the shipping time. Even with express shipping, you might have to ( ) a few days for your stuff to arrive. It's not great if you need Amy: Jake: Jake: Amy: Amy: Jake: Jake: Jake: something urgently. True, waiting can be frustrating. But what about the ( that sometimes the prices are higher online. It depends. I've found some great deals online, especially during sales. But you're right; in some cases, the prices can be a bit inflated, and you might end up paying more than if you bought it in-store. Amy: And returns can be a hassle, too. I had to return a shirt once, and the process took forever. It's not as easy as just going to a store and returning it on the spot. Yeah, returns can be a pain. Also, there's the whole security issue. You must be careful about where you're buying from to avoid scams or stealing your ( ). Amy: Oh, definitely. I always make sure the website is secure before entering any payment details. 日本語 L ), you know? No need to leave the On the bright side, online ( ) can be super helpful. I always check them before making a purchase. It gives you an idea of the product's quality and whether it's worth the money. Amy: That's a good point. I do the same. It's like having the opinions of a bunch of friends who've already ( ) the product. Jake: Exactly. So, while there are some drawbacks, I think the ( ) of online shopping, like the convenience and variety, outweigh the ( ) for me. Yeah, I agree. It's all about finding a balance and being cautious about where and what you're buying. )? I've heard

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Mathematics Senior High

46番の無限級数の問題です。なぜこれは2nと2n-1に分けるのでしょうか?

I am. 2b が収束 an "=1 =1 = Σan+ [bn n=1 n=1 00 =Σan-Σbn n=1 7 8 a n=1 81 n 46. 第n項をa=(-1)"-1 n+1 lima2n-1=lim (-1)2n-22n-1 1118 1 1-(-- 21/12) 2 limazn=lim(-1)2n-1. 818 であり、 よって, N 818 n 2 1 √2n 1 2n + この無限級数は発散する。 1 √2n -Xn + + ·+.... + 11-0 + 2n 2n+1 は振動し, 0 に収束しない。 数列{an} n ここで,lim V2 したがって, limT"=∞ よって, 無限級数 n=1 47. 部分和として,初項から第n項までの和T” を考える。 1 1 1 Tm= √2 √√4 √6 √2n 2n 1 =8 とすると □(1) 2"-2" 5n 1 2n 3 3 1 n=1 √ 2n =lim ・+・・・ =lim →:00 →:00 4 5 45 次の無限級数の和を求めよ。 2 n 2 2+ 1 + √2n +.... は発散する。 (2) 0の半径をとするとき コ (3) すべての円の面積の総和を求めよ。 によってかわる大12 =1 1 n ADD □/46 次の無限級数は発散することを示せ。 1 2 3 + ・+(-1)"-1_ 2 3 4 =-1 + ......+ □(2) Σ- n=1 1+(-1)" n n+1 を を用いて表せ。 数列{an}が0に収束しない an は発散する ·+... が成り立つ 1≦k≦nのとき, 1 1 √2k √2n 1 2n がn個 ⓒSn≦T" (n=1, 2, 3, …....) のとき, limS=∞ ならば, limT"= 818 を利用する。 ・教p.25 応用例題12 ・教p.26 例題 13 p.27 例 10 352 → 十・・・・・・ の収束 発散を調べよ。 353

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