なぜこのように変形できるのでしょうか？ 数列の問題です

-2S,=1·1+ 26-3 b」(34-1) = 40 3-1 B 山楽さ ニ 示 406」= 40 b,=1 よって b = 3"-1 C n22のとき S,=aibi+2akbe k=2 るあケ間さ .O =a」bi+2ae+1 bk+1 k=1 また 来事類さ 3S.= aabr3) =D&a.be1 k=1 k=1 n-1 =Eaabei ta,ba+1 (③. ③) k=1 0-のより) -2S, = aibi+と (ak+1-Qk) bォ+1-Qnbn+1 k=1 n-1 =aibi+2 (2·ba+1)-anbm+1 k=1 D n-1 =aibi+22·36k-anbn+1 k=1 P(-1) = aibi+ 26·ba-anbn+1 n-1 ニ k=1 よって n-1 -2S,=1·1+ 6-34-1_(2n-1)·3" k=1

漸化式を処理する時に、n≧2のときは公比のn-2乗になる理由がわかりませんでした。教えて欲しいです。

5)は 画 1 -an+1 =21 an+1 an+2 an+2-2an+1=→(an+1-2am) のように2通りに変形できるから, antは公比2の等比数列であり, an+1 {an+1-2an}は公比の等比数列である。 2 そよって,n22のとき, て an+1 2an a3 22127-2 6) n-2 去aカ+1-2aカ= (as-2a。) an+1 2/

Strange how animals can do that, isn't it? という文が長文ででてきたのですが、how strangeじゃない理由、文構造を教えてください🙇‍♂️

（）に入るのが何か教えてください！

(People in billions) てのもとになった資料です。レポート中の( )に入るのは何年でしょうか。 Do you know which country has the largest population in the world? Here is a graph that shows the population growth in India and Introduction Most Populous Countries 1.55 - 導入 資料の紹介 1.5 China. 1.45 According to the graph, the population of s 1.4 Body India will be larger than that of China from 1.35 説明 ). Then India will be the most populous country in the world. 1.3 2025 2020 (Year) 2030 I think that India will become more and 2015 Conclusion India China 感想や意見 more powerful in the world. 10 World Population Prospects (2017)

問題文の意味が分かりません。 2、3、7の少なくとも一つで割り切れる数とはなんでしょうか？

B問題 倍数の個数(3つの集合) 1から 100 までの自然数のうち, 2, 3, 7 の少なくとも1つで割り切 れる数は何個あるか。 1から 100 までの自然数のうち, 2の倍数, 3の倍数, 7 の倍数全体の集合を,それそ れ A, B, Cとすると n(A)=50, n(B)=33, n(C)=14 また, ANB, BnC, CNA, ANBNCは, それぞれ6の倍数, 21 の倍数, 14の倍 数,42 の倍数全体の集合であるから 8 O日( n(ANB)=16, n(BnC)=4, n(cNA)=7, n(ANBNC)=2 2, 3, 7の少なくとも1つで割り切れる数全体の集合は AUBUCであるから n(AUBUC)=n(A)+n(B)+n(C) 本の日 ーn(ANB)-n(Bnc)-n(CnA)+n(ANBNC) さ 350+33+14-16-4-7+2=72 (個)圏 -

こんな感じの訳で合ってますか？🙇‍♀️

Hideyuki Takano is an adventurous nonfiction extraordinary things, and then tell stories in an 高野秀行さんはどんな人で, 学生時代には area of Congo. He decided to search for it with other members. That became his first big expedition project. ; 何をしていたのでしょうか. writer. His motto is "Visit unexplored places, do: entertaining way."° So far. he has visited many places: P in such countries as China, Myanmar, Turkey and Somalia, and written books about the people living 3 there and their way of life. At his university, Takano belonged to the expedition club. One day, he heard that a mysterious monster P called Mbembe might Iive in Lake Tele in a remote 3 area of Congo. He decided to search for it with othor 3

foodとfoodsの違いを分かりやすく教えてほしいです！ 出来れば例文もお願いします

答え合ってますか？

寄りそうオウエンとムゼイ 9noY19 Until they met, both Owen and Mzee had been P lonely. As the weeks went on, they spent more time together. Now they swim together, eat together, and sleep next to each other.Owen even playfully rubs ス50 his nose against Mzee's neck, and Mzee stretches his neck forward happily. 3 Many animal scientists say that they have never seen such an amazing friendship betweena mammal and a reptile before. OThe reasons are unclear, and science cannot explain everything、VBut this story shows that animals of different species can care for each other.

至急です‼️ 英作文の添削をお願いしますm(_ _)m

thvorite masician.Ilke Hatena ver _much. Hatena makes the music The music they make is vebe Ike to talk abont Aan eKLiting. The rhuthm is interestihg. Yan will ncuar torget Connect all the songs. it Jou hear it. IH yoru he coms one mesAQe. But they dan 4 shaw their thces. I _don'4 knawi hoaw mony they Are. Naw, you can see it yaudtube. lou can sten their sona Yamejanai s, "Kodakega. And their CDs ure on sele. For these reasons, vecammened Cam see す On Hatan: Thank thor Istenina.

関係詞です。追加ですがこのふたつの問題もなぜ答えがどちらもＣになるのか教えて欲しいです！！

7. Many people criticized me, but I did what ( ). Ahought (a) I thought I was right (6)Vthought it was right (C) I thought was right o (d) I was thought right