已知1-1/2=1/2,1/2-1/3=1/6,1/3-1/4=1/12,...(3)若1/1X2+1/2X3+1/3X4+...+1/n(n+1)=19/20,则n=___已知1-1/2=1/2,1/2-1/3=1/6,1/3-1/4=1/12,...根据这些等式解答下列个题.(1)求解:1/1X2+1/2X3+1/3X4+1/4X5+1/5X6 (2)化简1/1X2+1/2X3+1/3X4+...+1/n
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已知1-1/2=1/2,1/2-1/3=1/6,1/3-1/4=1/12,...(3)若1/1X2+1/2X3+1/3X4+...+1/n(n+1)=19/20,则n=___已知1-1/2=1/2,1/2-1/3=1/6,1/3-1/4=1/12,...根据这些等式解答下列个题.(1)求解:1/1X2+1/2X3+1/3X4+1/4X5+1/5X6 (2)化简1/1X2+1/2X3+1/3X4+...+1/n
已知1-1/2=1/2,1/2-1/3=1/6,1/3-1/4=1/12,...(3)若1/1X2+1/2X3+1/3X4+...+1/n(n+1)=19/20,则n=___
已知1-1/2=1/2,1/2-1/3=1/6,1/3-1/4=1/12,...根据这些等式解答下列个题.(1)求解:1/1X2+1/2X3+1/3X4+1/4X5+1/5X6 (2)化简1/1X2+1/2X3+1/3X4+...+1/n(n+1) (3)若1/1X2+1/2X3+1/3X4+...+1/n(n+1)=19/20,则n=____
已知1-1/2=1/2,1/2-1/3=1/6,1/3-1/4=1/12,...(3)若1/1X2+1/2X3+1/3X4+...+1/n(n+1)=19/20,则n=___已知1-1/2=1/2,1/2-1/3=1/6,1/3-1/4=1/12,...根据这些等式解答下列个题.(1)求解:1/1X2+1/2X3+1/3X4+1/4X5+1/5X6 (2)化简1/1X2+1/2X3+1/3X4+...+1/n
1/n(n+1)=(n+1-n)/n(n+1)=1/n-1/(n+1)
所以(1)1/1X2+1/2X3+1/3X4+1/4X5+1/5X6 =1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6=1-1/6=5/6
(2)1/1X2+1/2X3+1/3X4+...+1/n(n+1)=1-1/2+1/2-1/3+...+1/n-1/(n+1)=1-1/(n+1)=n/(n+1)
中间的约掉了,就剩两头的.
(3)若1/1X2+1/2X3+1/3X4+...+1/n(n+1)=19/20,则n=__19__
哎,写在纸上就是比在电脑上方便一些.