1975-01-30 — Page 21

華僑日報 All

Series Prev Next Source

四期星

日十三月一年五七九一歷公年四十六國民中

Sinos p(x, y) is on the airola

x2 + 34 - 1459 2ý, +40

化文育教頁一第張六第日九十月二十年寅甲歷更

WAH KIU YAT PO 3 JAN

put nek+1 the last line becomes.

育教僑僑華

Therefore the chance oCITY HALI

1 ia divisible by 9

2+22+23+ ··· +2 = 2(2-1) Hance it is true for nik; it is also true for n k+1.

at the first trial

LD75

中學會考專欄!

terme

and the chance of 3 black at the second trial

(#12)

1) put: n=1,

L.H.S. R.H.S.-

新數單(十二)·謝國興。

MODERN MATHEMATICS (#12)

"Mathematical Induction:

• Prove by Induction

14345+ ******* +(21−1) =

1) put na D.H.9. = 1

R.H.S.

it is true for n } ii) Assume it is true for n=k:

.1.0.1+3+5+

Hence

+(2k-1) = x2

Add (k+1)m temize: (2x+1) to.

both sides.

1+3+5+ •••• +(2k-1)+(2k+1)

= £ 2 + (2k+1)= (1+1)2;

Hence it is true for nal

11) Assume it is true for n-k

·2-3 + 3-4

Add:(c+1)th.

term, i.e.

to both sides.

+ +34

therefore the chance of the compound event=43 *.

140

20449

9 can be made up in 4 ways, the, chance of throwing 9 is

10. can be made up in 3 ways, the chance of throwing 10 is

11 Can be made up in 2 ways, the chance of throwing 11 is

(16+1)(x+2)= = 1641 † (Ic+1) (1642) 12 can be made up in :1. way

k(k+2)+1

(k+1} {k+2)"

12. (k+1)(x+2)

put n k+1, the last line becomes

put nek+1, the last line becomes 22 + 273 +374 +

1+3+5+ •••••• +(2n-1) = n2

Thus if it is true for n=k, it i

aldo true for n=k+1.0

2. 2+22+23+

...... +2 = 2 (21)

i put n-1,

B.H.5. = 2(2-1)

Hence it is true for n=1.

ii) Assume it is true for n=k

Add (k+1)th tem, i-e. 2k+1

both sides.

2(2-1)+2+

* 2.12k+1

2-2k+ 2

能

培

Hence it a true for n=k also true for n=k+1.

2 Solution to Exercise 11

19 n(n+1)

The number of ways in which 3 balls may be down is:03 The mumber of ways in which 3 white may be drawn is C2

The number of ways in which 3 black may be drawn is Ca

chance of throwing 11-18.36

Now the chance of throwing a. number not less than 9 is the sum of these seperate chances.

the required: chance.

-3 The chance that the number is a multiple of 3 is 6, and the chance that it is multiple of 71; hence the required chance is no + 20

Exeroise: Prove by Mathematical

Induction,

•1•1 + 2:2! #3-3!

= (i+1){ = 3

(n+1)(n+2)(n+3)**** (2n) ··

2.1.3.5:

(2n-1)

數學科(十二)•

ADDITIONAL MATHEMANICS

Solution to Exercise 11.

1. Let (cos & + i sin 0)” –

cos ne i sin ne be trus for some positive integer

Then

(cob. +1 8in në)(óoë në+í sin në)

cos ne cose sin në sin e +i(sin ne cos ecos ne sin e) =.cos(x+1)@ + i sin(n+1)9... Thus, if the theorem is true for it is true for n+1, it is true for.

, and therefore it is true for all positive integers.

(1 + 1)20 + (1

=(1+211)

(21)10+ (-21)]

2. The tangent at (4,2) to the circle x+y2-14x=2x+40=0 is 4x+2y-7(x+4)− (y+2)+40=0

10.0 3x

1.0.

It meets the x-axis where

•*. The co-ordinates of T are(1o 0) Let x,y,) be the point of contad. of the other tangent from T to the circle. The tangent at (x, y) to the circle is

XXq+Y¥q =7(x+Xq )=(y+y1 )+40 = 0

11 on the tangent.

:10

1061 - -7(x, y)-3, +40

500

2(50-11x1).

13x2 - 1:16x4 + 256 (x-4)(13x, -64)

The point of contsot of the

second tangent from

号樂

0) to the circle is.

This is a geometric progress, ion with first tam x and

em of the first n terms

x2(1-x)

1)x+1

When x

and n

(2)- 23+ 14(2)

28(2)-13

Since 2-10

-10

<0.001, the value of the

above expression lies between 1.999 and 2.

Exercise 12

1. Sketch the curve, y=

Prove that the area bounded by the curve and the line y-3 is 310g:16.

In the triangle ABC, the angle A (-de a. right angle and B= 30%

Frove that r

3. A_straight line cute the curve.

yenxd at Pag and R. The tangenta

時怨

at P Q and R meet the curve agab at p

and R respectively.

Prove that r, q1 and R1 are:

collinear.

最飛歐卽

新機洲大鉅公献

片到司映

日

(幕闊彩七)座定速火

紐

華約

!疑懸!張緊!秘神!情色

狂奪

煞龍命

心兇神軟胆殺魂鏡俱案飄頭寒蕩

冷絕剌全

星

場無激部

狄阿

龍倫

美德麗梅

英龍一 0 勇虎江主鬥湖角

角主「子男奇海謀-

入肉會登凶財物富攻奪色劇性女幕體剌知神,,孀心命情作慾煞計龍迷家狂星之關殺她便各別

華僑文化

·在大會堂梨房出售。心」。是次三場音樂會,門質分四元、五元、七元半,十元,及學生票二元。除「卡門」選曲外,中國歌典包括:新:安南、東各地民歌此外

·套管弦樂團再演奏「白毛女」交响詩,及另一首作品「英雄系碑 ,佳評如鄰。是次音樂會,適逢藝術節舉行期間,節目特別署度中國作品 :. 本港集古齋,自

繼續更換新展品

•集古齋春節畫展集體春節驚喜長以來

亦會透過往外地表演。在紐西蘭各地大城市演唱「蝴蝶夫人」及「天皇「去年七月,更與港管弦樂團合作,演唱「茶花女」及「蝴蝶夫人」選曲唱會獨唱部份,包括:凡爾第「安魂曲」及貝多芬「合唱交響曲」。江棒八大利聖茜茜莉亞學院深造。畢業後,回港舉行多次演唱會;及擔任聖樂演在港隨胡然教授學習鑿業。一九五六年:獲佛教音樂院文憑。次年,花惹首作品「白毛女」,與「英雄墓碑」。江女士在泡出生及接受激育。早年顾各地民歌四首;其他項目包括:朱變耳所作「節日序曲」,及梁維之兩

·演出,女高音江柳女士担任演唱歌劇「卡門」選曲三首;此外,並演唱中八時半,十五及十六日下午二時中,是大音樂會,由林克昌推揮港管弦樂團農曆年初四至初六),在大會堂音樂廳合辦三場音樂會,時間爲十四晚七 (港)市政局,香港安協及藝術節協會,將於二月十四至十六日(

市局管協與藝術節協會

合辦藝術節音樂會

江樺演唱中西歌曲

,由於展品豐富,吸

並設古籍特價部 *更換一批新國品,

中藥古帖

理價

,要買平書,此其時矣。該地址在中與雲咸街號南華大厦一樓,有葉便宜。不少學者、教授、大專同。特倎日有新的特價書補-

部偏要,飛磁集成苓本五折,並設有古籍特價部,供應大批時價書,價格 -

實。在展窮開門,將古籍書,碑帖册全部八折端硯石章七折,四有辦「人際關係座一半,假干中公教社

使這次展範內容更加

兩個聖母軍區

辦人際關係講座

聖母軍團員及倍友加而有語力的生活。歡迎識別人,建立積極 ,主題媵承認識自我,

(新龔肚)天主浟之母柩團,二月十八起

專家主購歡迎參加

·九龍協和書院校長邱 2 第一鹊 -- 二月十八日

聖母軍督察逛團及教會一一迩個星期二晚七時一何恩德講「人格的發展」

眼邱日加迎

大爆醜聞大爆內幕

熱門題材心照不宣

,者夫女,刦居,

賓係親是煞是有墅情險摸

看宜不童兒

問幾,性虎色心-

你難凡色視,,滿

未免發狂眈個是秘

?。生,都謀人,

怕倖有情况個不神淫送有

些吓 THE BIG

CONSPIRACY

光華國國油寶聯金麗太永皇皇

華都際寶地蔴聲邦門聲平華都

映公重隆綫全日全

「有未所前片國幕銀上彈實槍眞,片影的性炸爆满-

部

孚造大奇金其捨講獨唯黶

型海景三

梟

·桌菜。角誰我座等我片

漢卓黃

宜不意兒

FIRST PILNS

張陳陳

力敏星

主領皇

演銜牌條

江洪

慨捐響

|時代曲合唱團

此會籍利署劉啓在麇

婚四女母筆

糖

心

·锤姻心罊三化·利

第

每晚七時半至九時,服務中心報名。培道聯愛春節派米請各界解囊响應善舉

)。第二講,坻五日,一」,隱隱者可向所屬近一半,或向敦五牾楼

庭江日

,腰帶豬,顧及清香現發動請求捐助運動, 茜督致培达警愛奋,事善致,購米服濟。

五李治云。一九三九截止收獄,如默的, 王元分來,她把月五日合唱團、第三居新職骨家爲名譽顧問。參加辦

| 張歌唱藝術並榮音樂名寶麗來辦公開攝影賽 ,種善舉。在斤米阮港第一組成之時代曲音樂學院選出,昨在團址舉行就洪:可附酒倍封邀客

·新職員就任由團事委會主席潘邦俄索就及報名崴、成電H 職業爾程,捆林及區,為郡北角以巨大厦十一

用用觀公區

最之業開公

新相南蓋司費

養機瓶影特質

「不要辦來,

一、材分翩

定公司

型使使及的有本開

原不黑月攝

底影

館截賽

典·臣角放

范侠天天林件

海曦十寄運攝

各髁推廿冠界一林大畑名六, 攝辦貴名照人欲魚五

器及蜓手選。是黑材表多品及,段賽自店格欸器榮刚時宠正梁。富釋瓻本負

1975-01-30 — Page 21

Comments

Private Research Note