查看完整版本: pure mathz Ｉ08 10a

pure mathz Ｉ08 10a

唔明點解Ｐ（Ｘ）－Ｐ（Ｘ－１）既ＤＥＧＲＥＥ同個ＬＥＡＤＩＮＧ　ＣＯＥＦＦＩＣＩＥＮＴ係點出黎。

請post題目

p(x)=ax^k + bx^k-1  + ...

p(x-1)=a(x-1)^k + b(x-1)^k-1 + ...
         = ax^k   [color=Red]- [/color]a(kC1)x^k-1  [color=Red]- [/color]bx^k-1  +...
          =ax^k  [color=Red] - [/color](ka[color=Red] + [/color]b)x^k-1 + ...
since p(x) - p(x-1)=x^100
[ax^k + bx^k-1  + ...]   -  [ax^k  [color=Red]- [/color](ka [color=Red]+ [/color]b)x^k-1   + ...] =x^100
[color=Red](ak)[/color]x^k-1 + ...=x^100
leading coeff is k-1
k-1=100
k=101

[[i] 本帖最後由 36661124 於 2010-7-29 10:04 PM 編輯 [/i]]

唔好意思,有少少唔明.
甘個coefficient of x^k點解係1/101?

題目係
let p(x)be a ploynomial of degree k with real cofficients satisfying the following conditions
p(x)=p(x-1)+x^100
p(1)=1

find k and the coefficient of x^k in p(x)

p(x)=ax^k + bx^k-1  + ...

p(x-1)=a(x-1)^k + b(x-1)^k-1 + ...
         = ax^k  +a(kC1)x^k-1  + bx^k-1  +...
          =ax^k  + (ka + b)x^k-1 + ...

k=101
p(x)=p(x-1)+x^100
compare the coeff. of x^100 of both sides
b=ka+b+1
ka=-1
a=-1/101

[quote]原帖由 [i]傷愛[/i] 於 2010-7-29 07:41 PM 發表 [url=http://lsforum.net/board/redirect.php?goto=findpost&pid=2269787&ptid=145970][img]http://lsforum.net/board/images/common/back.gif[/img][/url]
唔好意思,有少少唔明.
甘個coefficient of x^k點解係1/101?

題目係
let p(x)be a ploynomial of degree k with real cofficients satisfying the following conditions
p(x)=p(x-1)+x^100
p(1)=1

f ... [/quote]
上面有少少錯(+ - SIGN)
睇返上面 同PETER 個POST 改返正負就得

[[i] 本帖最後由 36661124 於 2010-7-29 10:06 PM 編輯 [/i]]