1/1*2+1/2*3+1/4*5.1/49*50的解法

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1/1*2+1/2*3+1/4*5.1/49*50的解法

1/1*2+1/2*3+1/4*5.1/49*50的解法
1/1*2+1/2*3+1/4*5.1/49*50的解法

1/1*2+1/2*3+1/4*5.1/49*50的解法
=(1-1/2)+(1/2-1/3)+...+(1/49-1/50)
=1-1/50
=49/50

=1-1/2+1/2-1/3+1/3-1/4+……+1/49-1/50
=1-1/50
=49/50

1/1*2+1/2*3+1/4*5.....1/49*50
=1-1/2+1/2-1/3+1/3-1/4+...+1/49-1/50
=1-1/50
=49/50

1/1*2=1-(1/2)
1/2*3=(1/2)-(1/3)
……
1/49*50=(1/49)-(1/50)
所以1/1*2+1/2*3+1/4*5.....1/49*50
=1-(1/2)+(1/2)-(1/3)+……(1/49)-(1/50)
=1-(1/50)=49/50