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数学 高校生

29番の(1)で必要十分条件を求める問題で、どちらが必要条件でどちらが十分条件か分からなくなってしまいました。考え方を教えて頂きたいです。

28 よって ここで ゆえに −(n=k+1}{n+k+1)+(n−k)(n+k) n→∞0 =-2k²+(2n²+2n+1) f(n)=-4 f(x)=x(2k² +2n² +2n+1) k²=0+22k², 1=2n+1 TA³5 k=1 −42 k²+(2n²+2n+1) (2n+1) k=1 − n(n+1)(2n+1)+(2n²+2n+1)(2n+1) lim 72-00 n³ (2) f(n) -1/(1+1/2)(2+1/2)+(2+1/2)(2+1)} =--²--1-2+2-2= 8 3 3 別解n≦x≦k, k≦x≦n と k<x<kに分けて,直線 y軸に平行な直線につ x=i (-n≦i≦n) 上にある格子点の数を求める。 さて格子点を数える。 = -n≦i≦k のとき, 格子点の数は k=-n 1+3++{2(n−k+1)−1}=(n−k+1)² = (+_____________ k<i<kのとき, 直線 x = i の本数は ←-k+1≦isk-1 各直線上の格子点の数は よって k-1-(−k+1)+1=2k-1 = I=gb S=b 2(n-k+1)-1=2n-2k+1 Nk=2(n-k+1)+(2n-2k+1)(2k-1) =-2k²+(2n²+2n+1) 総合を複素数とする。 自然数nに対し、2” の実部と虚部をそれぞれxとyとして、2つの数列 29 {Xn},{yn}を考える。 つまり, z=xn+iy" (iは虚数単位) を満たしている。 (1) 複素数zが正の実数と実数0を用いて z=r (cos0+isine) の形で与えられたとき、 数列{x},{ym} がともに0に収束するための必要十分条件を求めよ。 1+√3 10 = n(n+1)(2n+1) のとき、無限級数Σx とΣy はともに収束し, それぞれの和は n=1 71=1 x=2y=イロである。 (1) z=r (cos0+isin0) [r>0] のとき HINT (1) x²+y² = (r")2 となることに注目し, まず必要条件を求める。 (2) z を等比数列の和の公式を利用した式で表してみる。 ORAN z"=r" (cosnotisinn()=r"cosn0 +ir” sinne Xn=r" cosnd, yn=r"sinno よって ゆえに x2+yn²=(r")' (cos2nd+sin'nb)=(x2)" limxn=limyn=0のとき lim(x²+ym²)=0 〔類 慶応大] 本冊 例題 13,102 ←ド・モアブルの定理。 ←=xn+iy 0sr²<1 よって に0<r<1のとき 1-400 0<r<1より, lim|rl"=0であるから ゆえに 0≦|x|=||"|cos nolsrp. よって 0≦ly|=|||sinner| また 以上から、求める必要十分条件は +③iのとき 10 lim|x|=lim|y|= 0 71-00 ゆえに 1110 Z ここで1-2 lim xnn-000 ZR= ここで k=1 z(1-2)= 1-² よって 1- 1+√3 i 10 1+√3 i 10 k=1 84 3+5√3 i 42 (1+√3i)(9+√3 i) (9-√3i)(9+√3 i) 6+10√3i_3+5√3i 2x= k=1 1-2 (1-(xn+iyn)) 1+√3 i 9-√3i 11-0 0721 0<r<1 n=1] -(1-Xn-iyn) 2R= = 1/2 (3(1-xn) +5√3 yn+(5√/3 (1–xn)—3yn}i) z*= (xn+iyn)= xx+iZyn k=1 3(1-x₂)+5√√3 yn 42 ΣXn² n=1 42 5√3 (1-xn)-3yn 42 0</1/3 <1であるから, (1) の結果より limxn=limyn = 0 „=lim 11-00 2 k=1 2 = = = = ( 1²/2 + √²³_i) = = = (cos / 1 + isin) Σyn=lim- 11-0 ←Sa<1のとき a²19 a=1のとき、 α>1のとき、18 42 ←xel Saxolxel から、 xel 0のとき 初項z. 公比zの等比 数列の初項から第 環 までの和 12-00 3 (1-x)+5√3ym_3_71 42 5√3 (1-xn)-3yn_15√/3 42 -419 ←分母の実数化。 42 14 ← 22 のもう1つの表現。 ←実部、虚部をそれぞれ 比較。 (12) 結果を利用 総合 N=1 £ =lim ży

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英語 高校生

答えを無くしてしまい丸つけをお願いしたいです。 多分中学生レベルの英語だと思うのですが英語はあまり得意ではないので合ってるか分かりません…。お願いします。

and ise yi galijquls og rhillOS DATOS A Grammar 1回目 2回目 参考書: pp.287~324/テキスト: pp.58~63 A Grammar BWriting /15 /15 NAVEGHENDA 1 Choose the correct word or phrase in the brackets. (1) 私にはいとこは1人もいません。 [一般動詞 (1語) の否定文] /25 /25 ■解答・解説書: pp.20~21 CReading 32の各文の下線部を尋ねる文を書きなさい。 (1) Where does Yuri work? (2) What did Roi make? (3) When is her birthday? (4) Who did write this poem? (5) How many beetles did Yuta catch? /8 /8 Total 148 /48 263 bribute irl dek«) (0) I [ haven't/ don't have any cousins. (2) 予定は変更されないだろう。 [それ以外の否定文] (1) The schedule [ will be not/ will not be ] changed. (3) その部屋にはエアコンはありましたか。 [一般動詞(1語)の疑問文] [Had the room / Did the room have ] an air-conditioner? (4) あの魚は英語で何と呼ばれていますか。 [それ以外の疑問文 ] What is that fish called / is called that fish ] in English?di bad og 576 (5) これが何だか知っていますか。 [間接疑問] dunibor Brw of this ootisli snob bila Ind Do you know what [ this is/is this ]? noo gniwollo) ert bes à bns notice of veinque i ind W politiq a to attrrent oli jon otamso tanī sablick: Ting nguo & bas 1979) s hari semas all bad oolele lid ② 各文の下線部を尋ねる疑問詞 (1語または2語) を答えなさい。 (1) Yuri works at a hospital. (ユリは病院で働いている)[場所] (where (2) Roy made a doghouse. (ロイは犬小屋を作った)[物]ei woled songinsa do (what (3) Her birthday is June 20. (彼女の誕生日は6月20日だ [時] (4) Sayaka wrote this poem. サヤカがこの詩を書いた) [人] A diw to (when (who (5) Yuta caught five beetles. (ユウタは5匹のカブトムシをつかまえた) [数] B 1 C (how many)

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英語 高校生

2を教えてほしいです💦お願いします🙇

英語 ( 70分) 1 次の文章を読んで 1~7の問いに英語で答えなさい。 It's Christmas Eve, December 24, 1914. The night is clear and cold/ Moonlight illuminates the snow/covered land separating the British and German trenches outside a small town in northern France. British military command feeling nervous sends a message to the front lines: it is thought possible the enemy may attack during Christmas or New Year. Extra caution will be maintained during this period. The military command has no idea what's really about to happen. Around seven for eight in the evening/ British soldier Albert Moren blinks in disbelief What's that on the other side? Lights flicker on./ one by one. Lanterns. he sees, and torches, and... Christmas trees? /"Stille Nacht, That's when he hears it - soldiers singing in German/" heilige Nacht." Never before had the Christmas music sounded so beautiful. I shall never forget it," Moren says later. It was one of the highlights of my life. Then, in response, the British soldiers start singing The First Noel." The Germans applaud, and counter by singing "O Tannenbaum." They go back-and-forth for a while, until finally the two enemy camps sing "O Come, All Ye Faithful" in Latin, together. "This was really a most extraordinary thing." soldier Graham Williams later recalled, "two nations both singing the same Christmas music in the middle of a war." Events just north of a small town in western Belgium go further still. From the enemy trenches, Corporal John Ferguson hears Someone call out, asking if they want some tobacco. "Come towards the light," shouts the German. So Ferguson walks out into no-man's land into the field between both armies. "We were soon speaking as if we had known each other for years." he later wrote. "What a sight little groups of Germans and British talking together almost as far as the eye can seel Out of the darkness we could hear laughter and see lighted matches.... Here we were laughing and chatting to men who only a few hours before we were trying to kill!" The next morning. Christmas Day, the bravest of the soldiers again climb out of the trenches. Walking past the barbed wire, they go over to shake hands with the enemy. Then they wave "come on!" to those who'd stayed behind. "We all cheered." remembered soldier Leslie Washington of the Queen's Westminster Rifles. "and then we all came out together like a football crowd." (A Gifts are exchanged. The British offer chocolate, tea and cakes: and the Germans share cigars, sauerkraut and schnapps. They make jokes and take group photographs as though it's a big./happy reunion/ More than one game of football is played./using helmets for goal posts. One match goes 3-2 to the Germans, another goes to the British, 4-1. In northern France/the opposing sides hold a joint burial service. "The Germans formed up on one side." Lieutenant Arthur Pelham- Burn later wrote./"the English on the other, the military officers standing in front, helmets off, heads bowed in respect. As their friends are laid to rest friends killed by enemy bullets - they sing in English "The Lord is My Shepherd" and the same song in German mein Hirt" their voices in unison. "Der Herr That evening, there are Christmas dinner parties up and down the lines. One English soldier finds himself invited into the German held zone to a wine cellar, where he and a soldier from southern Germany pop open a bottle of 1909 French champagne. The men exchange

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英語 高校生

高校英語の比較のよくわからなかった問題です 答えとできれば簡単な解説をお願いします

5) blugp,bluow). 2 Complete a new sentence with a similar meaning. Soccer is the most popular sport in the world. No other sport in the world is as TIJE popular as soccer. is as popul in evi 1) Soccer is the most popular sport in the world. 4) 命ほど大切なものはない。 URSORS) +2+N [asw] stow AKO led Furth nbluow nifee POSICIER tikk. Jenif and on bein [nothing, life, precious] stel omso er ti ld is more. No other sport in the world is more 2) Makoto can jump the highest in our team. No one in our team can jump as 3) Sae finished the test the quickest of all the students in the class. sest of all 1 Jeroe2 ria it.E O Sae finished the test noom llut s moge ever blyos ew tripin tesi benis ton bad ti ll.A the test quicker t 3 Choose the better option. 1) Which is (the better / better) of the two plans? 2) Unfortunately, no (more/less) than fifty people were injured in the accident. 3) This village is very small. There are not (more/less) than twenty houses in it. 4) Getting enough sleep is no (more/less) important for health than nutritious* food. nee bonutritious 「栄養のある」 AND! an 11 4 Put the Japanese sentences into English. Use the word in the brackets. 1) アラスカはアメリカのどの州よりも大きい。 [any, state] Unca JASNOST Alaska is 2) 雨が降っているので、 外出するより家にいたい。 [prefer] It's raining, so 3) ジャックはたった1年でスペイン語を習得した。 [more, master] pniwanb (▶6 (▶5-2) in the US. od now I reiw 1.8 new1.c RX KERAL PO HEWOR gniwerb to boop lon mis I (tarii) yrios ma 1-a

未解決 回答数: 1