以下の画像の問題についてです。 ｢収束半径内で f(x) ＝ x/(1－x－x²) であることを示せ｣ の部分の解き方が全く分かりません。ヒントだけでも良いので、教えていただけないでしょうか？ ちなみに使うかどうかは分かりませんが、収束半径は (√5－1)/2 です。

問題 1.10. フィボナッチ数列, ai = a2 = 1, an+2 = an+1 + an, n >1 を考える。 この時,べき級数 f(zx) = >) ana" の収束半径を求め、収束半径内で f(z) = で n=1 あることを示せ。 をベキ級数に展開する事を考える。収束半径内でベキ級数の係数が一意である 1 1-2-22 事から,フィボナッチ数列の一般項を求めよ。

英検準一級の英作文の添削をして頂きたいです。見にくいところがあれば言ってください。よろしくお願いします。

Date No. Topic: Is the recent increase in the nigyber of penple changing jobs in Japan a pasitive development Y I de not think that the recent increase in the. number of people 15 (7 changingjobs in Japon is a pasitive develepnet, I have reasons to support my opinion in terms of effect on the economy and unenplymoant Fict if the number of peaple changing jobs increases, Some Companies will in Jopan. Eflect on the economy will larger than before. bankrupt. It would be a serious problem Second, it is dificult for them to change their jobs becouse theyshould remenber new job Companies do not have enough time to teach working and people changing jo would be tired to remember. I think companies Could not get s. adventagpe For these reasons, the number of people changing jobs in Japan is a negative develapmat. (123 words)

英検の英作文の添削をお願いします。見にくいところがあれば言ってください。

Dat ici Agre or disagree Elderly pegle Should be taken core of by their rather than sent to nursing homes I agre with the idea that elderly pesple should be taken Cae of by their tailies rater fhen Seat to nursingg homes, I have Two reasons To suport may opinjon in Tecms of better core and financial burdon r on family. Fist, families con be berer core than nursing homes because they know abart elderly faily members mme. If nuring homes tale Care of elderly pople,they con not be the best support. L It is easy for families to take care of them. Secondi Senting to nursing hemes Cost mare. If eldery paple are taken core of by nursing home s, thair families have to pay charge. It is difficat to pay high fee. for these reasons, elderly people should be taken care of hot y neriag homes but by their foniliea

丸つけたところ答えです。 どれか一つだけとかでもいいので、 問題の解説お願いします！！

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この問題4.1の証明が分かりません。分かる方がいればお願いします。

問題 4.1 U1,…,U, をベクトル空間V の部分空間とするとき, U」+ U2+…+U, = {a」 + a2 +……+a,|a, e U,, i= 1,2, …,r} となることを示せ。 問題 4.2 U1,…,U,をベクトル空間Vの部分空間とする.次の条件が同値であることを示せ、 (1) Ui +…+U,が直和である。 (2) a1 + a2 +…+a, = 0 (a; E Ui) ならば aiは全て0である。 (3) 任意のiに対して,U;n (Ui +…+U,) = {0}.

韓国語で書かれた文章です。どなたか和訳をお願いします🙇‍♀️

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韓国語の文章です。どなたか訳をお願いします🙇‍♀️

0|回召全全 20| 日 合LIC. 2C個回92 | }全20|回 全以合LC, 早卒人に望00 0|21OL 04丘LC.

(ii)と(iii)がどうしてこうなるのか分かりません お願いします

b. [1+] Let t(n) be the number of total partitions of n, as defined in Exam- ple 5.2.5. Let g(n) have the same meaning as in Exercise 5.26. Deduce from (a) that g(n) = 2"t(n) for n >1. c. [2+] Give a simple combinatorial proof of (b). 5,37. a. [2+] Let 1=D po(x), pi(x), be a sequence of polynomials (with coeffi- cients in some field K of characteristic O0), with deg pn=n for all nE N. Show that the following four conditions are equivalent: ) Pn(x + y) =DE>o (") Pe(x)pnーk(y), for all n eN. (i) There exists a power series f(u)=aju+azu'+ E K [[u]] such that と P(x)- un expxf(u). (5.110) n! n>0 仮定 NOTE: The hypothesis that deg pPn=nimplies that aj ¥ 0. () E20 Pa(x) = (E>0 Pn(1)). (iv) There exists a linear operator Q on the vector space K[x] of all poly- nomials in x, with the following properties: ●Ox is a nonzero constant ●Qis a shift-invariant operator, i.e., for all aeK,Qcommutes with the shift operator E4 defined by E® p(x)=D p(x +a). ● We have Qpn(x) =D npn-1(x) for all n e P. NOTE: A sequence po, Pi, .. . of polynomials satisfying the above con- ditions is said to be of binomial tvpe. The operator Q is called a delta

赤く印したところ同士が同じものを示しているのはわかるのですが、なぜA×Bがこれらの式で表せるのかわかりません。なぜですか

5) A= Ai+Ayj+A,k, B= B,i+Byj+B,k ならば A×B= (A,B,-A,B,)i+(A;B.-A,B.)j+(AzB,-A,B.k (2.1) 5)は4)を使って示すことができる。 行列式(2-4 節で述べる)の記号と思いれば, ペクトル積は、 |4, A, j+ Bs |Az A |Ay A.| B。 Bu A×B- B, B。 三 i j k (2.8 =| A』 A, A,

解き方を教えて欲しいです🙇‍♀️

問題。 Rr, 2yry|| nE Z20, aij € R 0<Sn と定めると,Rlと同様に可換環となる。このとき,この環は単項イデ アル整域ではないことを示せ。