funny maths question

2011-11-21 2:13 am

1/3 = 1+3/5+7 = 1+3+5/7+9+11 = 1+3+5+7/9+11+13+15 = .............

Why this appear? proved it.
偶數有類似情況? proved it why or why not.

回答 (2)

用戶27207

2011-11-21 5:48 am

✔ 最佳答案

1/3 = 1+3/5+7

??!!

2011-11-20 19:40:38 補充：
哦……………………………

2011-11-20 21:48:18 補充：
Let T₁=1/3,(1+3)/(5+7),(1+3+5)/(7+9+11),… T₁(1)=1/3T₁(2)=(1+3)/(5+7)T₁(3)=(1+3+5)/(7+9+11)…T₁(n)=[1+…+(2n-1)]/{(2n-1+2)+…+[2(2n-1)+1]}T₁(n)=[1+…+(2n-1)]/[(2n+1)+…+(4n-1)]T₁(n)={[1+(2n-1)]n/2}/{[(2n+1)+(4n-1)]n/2}T₁(n)=[1+(2n-1)]/[(2n+1)+(4n-1)]T₁(n)=(2n)/(6n)T₁(n)=1/3

Let T₂=2/4,(2+4)/(6+8),(2+4+6)/(8+10+12) T₂(1)=2/4=T₂(2)=(2+4)/(6+8)T₂(3)=(2+4+6)/(8+10+12)…T₂(n)=(2+…+2n)/[(2n+2)+…+2(2n)]T₂(n)=(1+…n)/[(n+1)+…2n]T₂(n)=[(1+n)n/2]/{[(n+1)+2n]n/2}T₂(n)=(1+n)/[(n+1)+2n]T₂(n)=(1+n)/(1+3n)

2011-11-20 21:58:57 補充：
So,

T₁=1/3

T₂(n)=(1+n)/(1+3n)

參考: Hope I Can Help You ! ^_^ ( From Me ), Hope I Can Help You ! ^_^ ( From Me )

👍 0 👎 0

Lll

2011-11-21 2:44 am

1/3
=(1+3)/(5+7)
=4/12
=1/3

👍 0 👎 0