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標題: A maths 幫下手.... [打印本頁]

作者: orienteerer 時間: 5/1/2005 08:44 PM
標題: A maths 幫下手....
A maths~　MI(mathematical induction 數學歸納法)...

條數就咁ge... (我EMI... 得english ja... 最好唔好問我中文解番條question...)

Prove by mathematical induction that if n is a positive integer,
f(n) = 3^(2n) - 1 is divisible by 8.

我諗最好都係問問版主smallpotato226大佬 la... =.="

我係俾個 f(n)搞到唔識做姐... =.=" only幫我搞到lei舊野都ok ge la...

[ Last edited by orienteerer on 2005-1-5 at 08:46 PM ]

作者: 抹茶可樂 時間: 5/1/2005 08:58 PM
Let S(n) be the statement "f(n) = 3^(2n) - 1 is divisible by 8." .

Prove S(1) is true,
f(1)=3^(2x1) - 1 =8x1
S(1) is true.

Assume S(k) is true,
f(k)=3^(2k) - 1 =8M, where M is an integer.
　　9^k =8M + 1

Prove S(k+1) is true,
f(k+1)
=3^(2k+2) -1
=9^(k+1) -1
=9x9^k -1
=9(8M+1)-1
=72M+8
=8(9M+1)
S(k+1) is true.

By the principal of mathematical induction,
S(n) is true for all positive integers.

作者: oscar 時間: 5/1/2005 08:58 PM
Let f(n) be the proposition '3^(2n)-1 is divisible by 8'
When n=1,
3^2-1=8 which is divisible by 8.
So, f(1) is true.
Assume that f(k) is true.
i.e. 3^(2k)-1=8M, where M is an integer.
When n=k+1,
3^2(k+1)-1
=3^2*3^(2k)-1
=9*3^(2k)-1
=9*[3^(2k)-1]+8
=9*8M+8
=8(9M+1)
So, f(k+1) is true.
By the principle of MI, f(n) is true fpr all positive integer.

作者: 抹茶可樂 時間: 5/1/2005 09:00 PM

oscar 在 2005-1-5 08:58 PM 發表:

Let f(n) be the proposition '3^(2n)-1 is divisible by 8'
When n=1,
3^2-1=8 which is divisible by 8.
So, f(1) is true.
Assume that f(k) is true.
i.e. 3^(2k)-1=8M, where M is an integer.
Wh ...

你入了陷阱，
f(n)=3^(2n)-1 和
f(n)=the proposition '3^(2n)-1 is divisible by 8'

是不同的 (- -")

另外，留意下我做MI的方法，有不同的。

[ Last edited by 落雷 on 2005-1-5 at 09:02 PM ]

作者: oscar 時間: 5/1/2005 09:00 PM

落雷在 2005-1-5 20:58 發表:

Let S(n) be the statement "f(n) = 3^(2n) - 1 is divisible by 8." .

Prove S(1) is true,
f(1)=3^(2x1) - 1 =8x1
S(1) is true.

Assume S(k) is true,
f(k)=3^(2k) - 1 =8M, where M is an ...

剛剛比你慢數十秒發帖...
極無奈...

作者: 貝貝☆ 時間: 5/1/2005 09:08 PM

登錄/註冊後可看大圖

Sorry因為太興奮
做哂成題

[ Last edited by ericfong on 2005-1-5 at 09:19 PM ]

作者: oscar 時間: 5/1/2005 09:23 PM

ericfong 在 2005-1-5 21:08 發表:

登錄/註冊後可看大圖

Sorry因為太興奮
做哂成題

你係唔係中五呀？
因為我見到你張紙上有limit...

作者: 貝貝☆ 時間: 5/1/2005 09:26 PM

oscar 在 2005-1-5 09:23 PM 發表:

你係唔係中五呀？
因為我見到你張紙上有limit...

佢係我呀哥
冇讀A maths不過讀緊pure maths

佢超勁

係學校今次考試全級第1-.-

作者: oscar 時間: 5/1/2005 09:29 PM

ericfong 在 2005-1-5 21:26 發表:

佢係我呀哥
冇讀A maths不過讀緊pure maths
佢超勁係學校今次考試全級第1-.-

你中幾呀？
我阿哥都係中六，都係讀P. Maths.的~

作者: 貝貝☆ 時間: 5/1/2005 09:54 PM
中6
你呀哥邊間呀

作者: oscar 時間: 5/1/2005 09:55 PM

ericfong 在 2005-1-5 21:54 發表:

中6
你呀哥邊間呀

丘佐榮中學~
睇你個樣都唔會識嫁啦~

不過頭先o個題唔係我阿哥做...係我做...

作者: 抹茶可樂 時間: 5/1/2005 10:03 PM

ericfong 在 2005-1-5 09:26 PM 發表:

佢係我呀哥
冇讀A maths不過讀緊pure maths
佢超勁係學校今次考試全級第1-.-

佢讀邊間的…我也聽過這個特殊例子

不過大家千祈唔好試…死緊的

作者: 貝貝☆ 時間: 5/1/2005 10:07 PM
丘記都ban1 la
點會唔識呀
我呀哥個時填第2志願la都
不過派唔到ja ma唉....
我呀哥form 6轉左去新法XDDDDDDD死廢柴

作者: orienteerer 時間: 6/1/2005 12:38 AM
唔該晒咁多位先... 聽日番去咁又有hw交la...(x'mas個d...) =.="
thx for all... thx!!!~ :em48:

作者: Ron@MX 時間: 6/1/2005 12:40 AM

orienteerer 在 2005-1-6 12:38 AM 發表:

唔該晒咁多位先... 聽日番去咁又有hw交la...(x'mas個d...) =.="
thx for all... thx!!!~ :em48:

聽日先交 Christmas 功課！？..........=.=

作者: orienteerer 時間: 6/1/2005 12:51 AM

我想做好人 在 6-1-05 00:40 發表:

聽日先交 Christmas 功課！？..........=.=

...係 =.="(汗...
but x'mas a.math要做十幾條MI+廿幾條binomal... math做廿幾條quadratic...
x'mas就梗係拎黎玩ge la... but仲得鬼閒做咩... 好彩ar sir都俾我最遲聽日先交... 都仲趕到... ＝＝"(暴汗...

作者: oscar 時間: 6/1/2005 11:13 AM

orienteerer 在 2005-1-6 00:51 發表:

...係 =.="(汗...
but x'mas a.math要做十幾條MI+廿幾條binomal... math做廿幾條quadratic...
x'mas就梗係拎黎玩ge la... but仲得鬼閒做咩... 好彩ar sir都俾我最遲聽日先交... 都仲趕到... ＝＝"(暴 ...

唉...真係懶到爆...
臨急抱佛腳...

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