数学Paper 1讨论专区

wuhu

MathType (Trial 30天)
kelfaru 发表于 19-10-2010 07:40 PM

   什么来的~看不懂~不好意识~

wuhu

哪本书的作业?
Allmaths 发表于 19-10-2010 08:08 PM

   我补习老师出的题目来的~

Allmaths

我补习老师出的题目来的~
wuhu 发表于 19-10-2010 08:12 PM

   原来...老师没给答案吗?

wuhu

原来...老师没给答案吗?
Allmaths 发表于 19-10-2010 08:13 PM

   有~就只有这样而已~a=5,b=-1 or a=-5,b=1~

Allmaths

有~就只有这样而已~a=5,b=-1 or a=-5,b=1~
wuhu 发表于 19-10-2010 08:16 PM

  这样的话我觉得题目真的错了...

wuhu

这样的话我觉得题目真的错了...
Allmaths 发表于 19-10-2010 08:20 PM

   可能咯~习惯就好~那老师是这样的~通常给的答案有时有错的~有时侯都受不了他~好才我没买他出的书要不然做不到答案我看我会越做越火大啊:@~

evildevil7n

1. Show that the geometric series 1+(e^-x)+(e^-2x)+...has a sum to infinity for any positive real number x. Given that x=10, write down expressions for Sn the sum to n terms, and for S, the sum to infinity. Given also that S-Sn<S/(10^100), show that n>10 ln 10.

2. Given that (1+x)^n = co+c1x+c2x^2+c3x^3+c4x^4+...+cnx^n for constants co,c1,c2,...,cn.
Show that (a) c0+c1+c2+c3+c4+...+cn = 2^n
               (b)(i) cr=cn-r where r=0,1,2,...,n                                   2n
                   (ii) co^2 + c1^2 + c2^2 +c3^2 + c4^2+...+Cn^2 = ( n )
3. (a) A circle which lies in the first quadrant touches the x-axis,y-axis and the straight line 5x-12y-24=0. Find the equation of the circle.
    (b) PO and RS are two chords of the rectangular hyperbola xy=c^2 and PQ and RS are perpendicular to each ohter. Given that the coordinates of P,Q,R, and S are (cp,c/p),(cq,c/q),(cr,c/r)and (cs,c/s) respectively. Show that PR is perpendicular to QS.

要考试了要考试了~~平时不烧香平时不烧香~~{:2_71:}{:2_72:}

wuhu

1. Show that the geometric series 1+(e^-x)+(e^-2x)+...has a sum to infinity for any positive real nu ...
evildevil7n 发表于 19-10-2010 08:49 PM

   跟我一样~我现在做数学做到火大~想哭啊~

evildevil7n

T.T..我不只是数学想哭。。。物理也想，PA真的是要吐了！！！

<cute~

Allmaths

1. Show that the geometric series 1+(e^-x)+(e^-2x)+...has a sum to infinity for any positive real nu ...
evildevil7n 发表于 19-10-2010 08:49 PM

    STPM出第二题大部分人死翘翘...

wuhu

T.T..我不只是数学想哭。。。物理也想，PA真的是要吐了！！！

{:3_10 ...
evildevil7n 发表于 19-10-2010 08:58 PM

   又遇到志同道合的人~哈哈~考试到要疯了~拜五考pa准备死~

kelfaru

回复 2067# evildevil7n

1)r=1/e^x
0<1/e^x<1
l r l < 1 for sum to infinity
1/e^x is in the range of -1< r < 1 (Shown)

a=1
r=1/e^x
Sn = a(1 - r^n)/1-r
x=10
Sn=[1(1 - (1/e^10)^n)]/[1-(1/e^10)]
   =(e^10)(e^10n - 1)/(e^10n)(e^10 - 1)
Sum to infinity
a=1
r=1/e^10
Sum to infinity
=a/1-r
=1/1-(1/e^10)
=(e^10)/(e^10 - 1)

Given also that S-Sn<S/(10^100), show that n>10 ln 10.
S-Sn>>>什么意思???

kelfaru

2. Given that (1+x)^n = co+c1x+c2x^2+c3x^3+c4x^4+...+cnx^n for constants co,c1,c2,...,cn.
Show that (a) c0+c1+c2+c3+c4+...+cn = 2^n
               (b)(i) cr=cn-r where r=0,1,2,...,n                                   2n
                   (ii) co^2 + c1^2 + c2^2 +c3^2 + c4^2+...+Cn^2 = ( n )

1. Show that the geometric series 1+(e^-x)+(e^-2x)+...has a sum to infinity for any positive real nu ...
evildevil7n 发表于 19-10-2010 08:49 PM

应该是 2^n - 1 吧???

Allmaths

Given that (1+x)^n = co+c1x+c2x^2+c3x^3+c4x^4+...+cnx^n for constants co,c1,c2,...,cn.
Show that (a) c0+c1+c2+c3+c4+...+cn = 2^n
               (b)(i) cr=cn-r where r=0,1,2,...,n                                   2n
                   (ii) co^2 + c1^2 + c2^2 +c3^2 + c4^2+...+Cn^2 = ( n )
evildevil7n 发表于 19-10-2010 08:49 PM

(1+x)^n = co+c1x+c2x^2+c3x^3+c4x^4+...+cnx^n
(a) Let x=1,


(1+1)^n = co+c1 (1)+c2(1)^2+c3(1)^3+c4(1)^4+...+cn(1)^n
2^n=co+c1+c2+c3+c4+...+cn   (shown)


(b)(i)用nCr=nC(n-r) 的特征

(1+x)^n=(nC0)1^n+(nC1)(1^(n-1))(x)+(nC2)(1^(n-2))(x^2)+...+(nCr)(1^(n-r))(x^r)+...+(nC(n-1))(1)(x^(n-1))+(nCn)x^n
           =1+(nC1)x+(nC2)x^2+...+(nCr)(x^r)+...+(nC(n-1))(x^(n-1))+x^n


所以:nC0=nCn

        nC1=nC(n-1)
          .       .

          .       .
        nCr=nC(n-r)



∴Cr=Cn-r




(b)(ii)Since Cr=Cn-r,
          Let S1=(C0)^2 + (C1)^2 + ... + (Cn-1)^2 + (Cn)^2
                   = C0 Cn + C1 C(n-1) + ... + C(n-1) C1 + Cn C0
                   = 2nCn

Allmaths

应该是 2^n - 1 吧???
kelfaru 发表于 19-10-2010 09:51 PM

是2^n没错...

kelfaru

是2^n没错...
Allmaths 发表于 19-10-2010 09:53 PM

看错东西,不好意思~

evildevil7n

回复  evildevil7n

1)r=1/e^x
0>什么意思???
kelfaru 发表于 19-10-2010 09:30 PM

S-Sn<S/10^100

kelfaru

S-Sn
evildevil7n 发表于 19-10-2010 10:11 PM

你的S是Sum to 什么???

Allmaths

你的S是Sum to 什么???
kelfaru 发表于 19-10-2010 10:15 PM

没有错的话应该是Sum to infinity...

Allmaths

1. Show that the geometric series 1+(e^-x)+(e^-2x)+...has a sum to infinity for any positive real nu ...
evildevil7n 发表于 19-10-2010 08:49 PM

    话说你这些题目不应该是STPM的standard...