Question

1x2分之1+2x3分之1+3X4分之1+……49X50分之1用简便方法

Answer 1

1X2分之1+2X3分之1+3X4分之1......+49X50分之1=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/48-1/49)+(1/49-1/50)
=1-1/50=49/50 1/（n*（n+1））=1/n-1/（n+1）

Answer 2

1X2分之1+2X3分之1+3X4分之1......49X50分之1=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/48-1/49)+(1/49-1/50)
=1-1/2+1/2-1/3+1/3-1/4+...+1/48-1/49+1/49-1/50
=1-1/50=49/50

Answer 3

1x2分之1=1-1/22x3分之1=1/2-1/33X4分之1=1/3-1/4……49X50分之1=1/49-1/50∴原式=1-1/2+1/2-1/3+1/3-1/4+1/4……+1/49-1/50 =1-1/50 =49/50

Answer 4

一般的：1/n(n+1)=1/n-1/(n+1)原式=1/1-1/2+1/2-1/3+1/3-1/4+,,,,,,,+1/49-1/50=1-1/50=49/50

Answer 5

原式=1-1/2+1/2-1/3……+1/49-1/50=49/50