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+..._数学解答

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=____

人气：409 ℃　时间：2019-10-23 16:36:33

解答

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...