A maths 幫下手....

orienteerer

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 ]

抹茶可樂

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.

oscar

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.

抹茶可樂

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 ]

oscar

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...

貝貝☆

                               
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 ]

oscar

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...

貝貝☆

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-.-

oscar

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~

貝貝☆

中6
你呀哥邊間呀