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数学 大学生・専門学校生・社会人

白チャート数IIIの数列の極限の問題です 2枚目の紙の☆→♡への式変形が分からないので解説をお願いします〜>_< (2枚目の紙は単純に白チャートに書き込みすぎてぐちゃぐちゃだったから書き直しただけです())

この命題の対側 (2) 無限級数 1+ + +...+ 1 3 n 命題が直 CHART ・対偶も & GUIDE ず再 ここで,m→∞のときぃ となる。 ∞ 発 例題 展 37 無限級数が発散することの証明 (2) (1)は自然数とする。1/12/10/ 1 2 <<< 標準例題22 ①①① k=1k +1 を数学的帰納法によって証明せよ。 1 ・+・・・・・・ は発散することを証明せよ。 無限級数が発散することの証明 (部分)> (∞に発散する数列)の利用 (2)(1)の不等式を利用する。 M 65 2 すると1/2 発展学習 2m 解答 1 n (1) k=1 k ・分子をnで割る。 IS [1] n=1のとき 1/2=1+1/2=1/2 {a} は収束するか 限値は0ではな (2)- 2m + 2k +1 ...... (A) とする。 '+1 ゆえに, n=1のとき(A) は成り立つ。 [2]n=m(mは自然数) のとき, (A) が成り立つ、すなわち1+1が成り 2+1 これをくり返し ( [ 「 m+1 立つと仮定すると n=m+1のとき ' 1 21 21 m 1 1 +1 + + k=k k=1k k=2+1k 2 2m+1 2m+2 2m+1 利 無限級 m +1+ + 1 2"+1 2m+2 1 1 ・+・ + 2"+2m -I' 例題 37 (2) m 1 m+1 +1+ •2m +1 2 2m+1 2 よって, n=m+1 のときにも (A) は成り立つ。 これを示したい [1] [2] から, すべての自然数nについて (A)は成り立つ。 21 (2) S=1/2" とすると, (1) から m +1 k=1 k k=1 k 2 ここで,m→∞のとき n→∞ m ゆえに limSlim n→∞/ るから, S である。」 よって発散する!! m n=1 n 2 E 621 1 d T TRAINING 1 37 ⑤ 00 2が発散することを利用して,無限級数Σ n=1 n m-00 2 追い出し +1=8 0 1+2+2 =2m+1 m 2°+2+2+2 m は発散することを示せ。 n=1 n 2m+2nt m [ 22 +2.2" M =2(

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TOEIC・英語 大学生・専門学校生・社会人

自分の回答があっているか不安なので、4第答えて頂きたいです。 自分の回答はこちらには見にくくなってしまうため書いていません。

Working with words 1 Complete the review of a hotel. Use the answers to complete the puzzle and find the European city where the hotel is located. HOTEL REVIEWS This first-class hotel and conference centre welcomes guests from all over the world. Its 1 facilities are second to none. There are 300 en-suite rooms and five apartment suites. For business guests, it has ten meetings rooms, two of which are big enough to be used as halls. 2 The hotel can also organize events such as guided 3 around the town centre for conference 4 and hotel guests who enjoy a bit of 5 For food-lovers, the four-star restaurant serves regional 6 every evening. All in all, this is a top-class for business and for pleasure. 7 6 1 A fa 0 il i t 1 e S 2 Replace the words in italics (1-8) with the phrases from the list. Add a pronoun if necessary. you hotel? look around meet up with show someone around 3 freshen up eat out pick someone up check in drop someone off Pedro It's difficult to park here. Can I stop and leave drop you off in front of the 1 Sabrina Sure, I'll register 2 and then I'd like to have a wash, and change my clothes 3 Pedro If you like, tonight I can give you a tour of 4 the old city. We could by eat in a restaurant 5 the port. Sabrina That sounds great! I'd rather walk about and See 6 the city than stay in my hotel room. Pedro I'll collect you 7 8 8.30 p.m. We'll see Alberto and Maite in the main square. at Business communication 1 Put the words in the correct order to make expressions. 1 meet person / it's / nice / to / you / in It's nice to meet you in person 2 have / did / finding / you/ any / trouble / us? 3 worry / signing / don't / about / in 4 through / programme / I'll / run / today's 5 this my / come / way / to / office 6 need building / you'll / this / enter / badge/ the / to 7 reception / sure / make / in / at / you / sign 2 Raymond Roberts has an appointment with Janet Rose. He has just arrived at HBG premises. Complete their conversation with the phrases from the list. let me take your bag can I get you a drink Welcome to HBG publishing I thought you could catch up again how was your journey You'll need this Make sure you 1 Raymond Good morning, I'm here to see Janet Rose. Janet Hello, I'm Janet. ¹ Welcome to HBG publishing. Raymond It's nice to meet you in person. Janet Likewise. So, 2 Raymond Well, there were traffic jams on the motorway and I got a little bit lost in the industrial park. Janet Don't worry. That happens to everyone. Anyway, 3 - I'll store it in my office. Raymond I'll hang on to it if you don't mind. It's got all my stuff in it. Janet Well, if you change your mind just tell me. And 4 Raymond Thanks. I'll have a cup of tea, please. Janet Sure, I'll just get that for you in a second. First of all, I'll run through the schedule. 5 start by meeting Karen Rankin this morning and then we'll 6 at lunchtime. Raymond OK. And will I see Malcolm Briscoe? Janet Yes, in fact he's joining us for lunch. One other thing. security pass. at all times. 7 It's your 8 wear it

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TOEIC・英語 大学生・専門学校生・社会人

訳して欲しいです至急ですお願いします🙏

s not something you Want 9 eir horme5・ It* 8 。 tak eople out of th 村 K you are ga ing 1 other than definitely needing to 9" 叶 dose 』 do lightIy , for 「@d rter to taKe shelter・ 1f is a plum, radiation・ Tn S0TTe accldents, IE 15 DTP indows 2 d or puf人 relea5e, people shelter In hou5e5 witl nt いい rhead2/" 58yS・ the puff has passed overheady Milligan 58Y : NeceSsarY changeS? In Japan, even the wake of the deadIy earthquake and ME d i ins25 We left local infrastructure ruin5, thousands of people た 抽 ta from the vicinity of the nuclear POWeT plant within 24 hourS・ MM 3 Milligan, dt least, does not anticipate anY chan9ges to the「Uu e5 ー し from27 less0nS learned from Fukushimaa ro nuclear DOWe「 plants stemmin9 now Provide adequate? ion for public| ww e Can See i ゞThe planning ZOneS in place There IS nothing W cate that We would need to expand、 zio る le health and safety,′ She SayS・ Fukushima meltdowns that would indi the_.plume eXxDOSU「 pathway“" an aircra介 mi ar USS Ronald Rea9 gase5?1 On ah dioactIVe noble e aircraft carrier found ほぼ: s for civilianS, after miles from the plant| e case of Fukushirma, the carrier? sailed into the plume of escaping「す March 12. More than 100 miles aWay, sailors on th jevels high enough to exceed the EPA'Sデ guideline zo roughly 10 hours of exposure. "They went up to 130 and we were St reading a direct gamma shine33 of 0.6 milirem pe 因 nour” explained the NRCS Stephen Trautman on March 12, according t9 s34. Garmma「ayS d「e among the most energetic 一 and tnerefore forms of radiation. Nevertheless, in th transcript dangerous tO health 一 2。 Tn the end, the question i5 One of risk. No one has died from radioactiwe contamination as a result of the Fukushima meltdowns, at least not yeW And it may prove impossible to disentangle3* any extra cancers due 0 Fukushima S radiation, from those that happen as a result of all the othW carcinogenic37 factors a DerSOn is exposed to in the modern world froW diet to smoke. But it remai i jns unclear how far radioactive emissions3 might reach In WW Case of a another 0 央0 1 Fukushima. "At that point its from We ? Another five miles? Another 10 miles? Do you 8 a Sense?” ask 1] Sked NRC chairman Gregory Jaczko on March 12, as he t his staff anal yzed computer modeling of a catastrophic meltdown す

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