先观察:-1x（乘号）1/2=-1+1/2-1/2x1/3=-1/2+1/3-1/3x1/4=-1/3+1/4.(1)你发现的规律:_______(用含N的式子表示ING,)(2)用规律计算:(-1x1/2)+(-1/2x1/3)+(-1/3x1/4)+...+(-1/2007x1/2008)
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先观察:-1x（乘号）1/2=-1+1/2-1/2x1/3=-1/2+1/3-1/3x1/4=-1/3+1/4.(1)你发现的规律:_______(用含N的式子表示ING,)(2)用规律计算:(-1x1/2)+(-1/2x1/3)+(-1/3x1/4)+...+(-1/2007x1/2008)
先观察:
-1x（乘号）1/2=-1+1/2
-1/2x1/3=-1/2+1/3
-1/3x1/4=-1/3+1/4
.
(1)你发现的规律:_______(用含N的式子表示ING,)
(2)用规律计算:
(-1x1/2)+(-1/2x1/3)+(-1/3x1/4)+...+(-1/2007x1/2008)
先观察:-1x（乘号）1/2=-1+1/2-1/2x1/3=-1/2+1/3-1/3x1/4=-1/3+1/4.(1)你发现的规律:_______(用含N的式子表示ING,)(2)用规律计算:(-1x1/2)+(-1/2x1/3)+(-1/3x1/4)+...+(-1/2007x1/2008)
(1)你发现的规律:_______(用含N的式子表示ING,)
-1/n×1/(n+1)=-1/n+1/(n+1)
(2)用规律计算:(需要过程)
(-1x1/2)+(-1/2x1/3)+(-1/3x1/4)+...+(-1/2007x1/2008)
=-1+1/2-1/2+1/3-1/3+1/4-1/4+.-1/2007+1/2008 (中间都正负抵消掉)
=-1+1/2008
=-2007/2008
(1)发现的规律:-(1/N)*1/(N+1)=-(1/N)+1/(N+1)
(2)(-1x1/2)+(-1/2x1/3)+(-1/3x1/4)+...+(-1/2007x1/2008)
=(-1)+1/2+(-1/2)+1/3+(-1/3)+1/4+...+(-1/2007)+1/2008
可以发现 有的可以互相抵消
=(-1)+1/2008
=-2007/2008
成功!!!!!!!!!!!!!!!!!
加油!!!!!!!!!!!!!!!!!
(1)-1/n *1/(n+1)=-1/n + 1/(n+1)
(2)原式=-1+1/2-1/2+1/3-1/3+1/4 ……-1/2007+1/2008
=-1+1/2008
=-2007/2008