mathematical induction problem (阿sir成功完美ko左條數)

天才A

小弟對數學都係一知半解...
但係應付8成課程既野都冇問題..
剩返2成問下老師都ok...
今次唔想等星期1再問..
所以係度問左先...

prove that by mathematical induction, that

5^(2n+1)-3^(2n+1)-2^(2n+1) is divisible by 30

咁前面果d冇難度 就ok la...

5^(2k+1)-3^(2k+1)-2^(2k+1) = 30m
之後 代 k+1 la...

得出
25．5^(2k+1)-9．3^(2k+1)-4．2^(2k+1)

之後雖然我好艱辛咁用左d白痴方法解到= = (再另外加多次 m i先得)
但係...
始終應該有個好方法
求大家既解
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呢個係阿sir 既解

做到 25．5^(2k+1)－9．3^(2k+1)-4．2^(2k+1)
之後抽19
19(5^(2k+1)－3^(2k+1)-2^(2k+1))+6．5^(2k+1)＋10．3^(2k+1)＋15．2^(2k+1)
19(30n)+30(5^2k+3^2k+2^2k)
30(19n+5^2k+3^2k+2^2k)

-終場ソ使者-

n既範圍係幾多先?n=1已經唔得啦-.-

p445hkk20001

n既範圍係幾多先?n=1已經唔得啦-.-
-終場ソ使者- 發表於 25-9-2010 03:07 AM

5^(2n+1)-3^(2n+1)-2^(2n+1) is divisible by 30
n=1 時 90 比30除到@@
佢應該係打錯

不過我估架@@

天才A

5^(2n+1)-3^(2n+1)-2^(2n+1) is divisible by 30
n=1 時 90 比30除到@@
佢應該係打錯

不過我估架@@ ...
p445hkk20001 發表於 25-9-2010 18:57

    !__!
係 +1= =
我打錯..

天才A

n既範圍係幾多先?n=1已經唔得啦-.-
-終場ソ使者- 發表於 25-9-2010 17:07

sor..
我打錯左 2^(2n-1)
其實應該係 2^(2n+1)
對唔住

-終場ソ使者-

喎,諗左好耐-.-
when n=k,

when n=k+1,
=
=
=
=
=
=


always be an even no. for all 5^2k, and 3^2k always being odd.
N-M=2P   (where P is an integer while N and M are odd no. with N>M)

p445hkk20001

唉我抽到去15, 抽唔到30
真失敗