1+2+4+8+16+...=-1 ??!!
2012-03-03 12:14 am
_1+2+4+8+16+...=(2-1)(1+2+4+8+16+...)=2(1+2+4+8+16+...)-(1+2+4+8+16+...)=2+4+8+16+32+...-1-2-4-8-16-...=-1 WHAT’SWRONG??!!
回答 (5)
2012-03-03 1:29 am
✔ 最佳答案
1+2+4+8+16+...=(2－1)(1+2+4+8+16+...)
=2(1+2+4+8+16+...)－(1+2+4+8+16+...)
=2+4+8+16+32+...－1－2－4－8－16－...
=－1
Sol
1+2+4+8+16+...
=(2－1)(1+2+4+8+16+...) =>正確
=2(1+2+4+8+16+...)－(1+2+4+8+16+...) =>錯誤
因為(1+2+4+8+16+…) 趨近於 ∞
我們不能寫成 ∞－∞
2012-03-03 3:16 am
Let x be the last number.
1+2+4+8+16+...+x
=(2-1)(1+2+4+8+16+...+x
=2(1+2+4+8+16+...+x)-1(1+2+4+8+16+...+x)
=(2+4+8+16+32+...+2x)-1-2-4-8-16-...-x
=x-1
As the result,we know that the answer should be (the last number -1).
But why?
It's because many people forget to use 2 times the last munber.Therefore,they will get (-1) as the answer after they finish it.
1+2+4+8+16+...+x
=(2-1)(1+2+4+8+16+...+x
=2(1+2+4+8+16+...+x)-1(1+2+4+8+16+...+x)
=(2+4+8+16+32+...+2x)-1-2-4-8-16-...-x
=x-1
As the result,we know that the answer should be (the last number -1).
But why?
It's because many people forget to use 2 times the last munber.Therefore,they will get (-1) as the answer after they finish it.
參考: myself
2012-03-03 2:30 am
上面岩
首先
如果1個1個term咁睇 2-1 =1 / 4-2=2 咁仍然都係1+2+4+8+16+...
其次
而上面講緊既就係
前面你有n咁多個term 後面減既個部分又有n咁多個term
如果你抽左-1 出尼 咁咪會變成n terms : n-1 terms
咁前面多左既term就會係抵消番d illusion
無論係邊個方法睇
obviously 唔係=-1 !
首先
如果1個1個term咁睇 2-1 =1 / 4-2=2 咁仍然都係1+2+4+8+16+...
其次
而上面講緊既就係
前面你有n咁多個term 後面減既個部分又有n咁多個term
如果你抽左-1 出尼 咁咪會變成n terms : n-1 terms
咁前面多左既term就會係抵消番d illusion
無論係邊個方法睇
obviously 唔係=-1 !
2012-03-03 1:04 am
1+2+4+8+... should be 1+2+4+8+...+2^n
in your calculation
1+2+4+8+...+2^n
=(2-1)(1+2+4+8+...+2^n)
=2+4+8+16+...+2^(n+1)-1+2+4+8+...+2^n
the answer is not -1!
in your calculation
1+2+4+8+...+2^n
=(2-1)(1+2+4+8+...+2^n)
=2+4+8+16+...+2^(n+1)-1+2+4+8+...+2^n
the answer is not -1!
2012-03-03 12:36 am
很明顯，no. of terms of (2+4+8+16+32+...) = no. of terms of (-1-2-4-8-16-...)
所以只以 (2+4+8+16+32+...) 抵銷 (-1-2-4-8-16...) 的話
(2+4+8+...) 最後的1個term 會出了多來~_~
所以只以 (2+4+8+16+32+...) 抵銷 (-1-2-4-8-16...) 的話
(2+4+8+...) 最後的1個term 會出了多來~_~
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原文連結 [永久失效]:
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