1/1*2+1/2*3+1/3*4+…+1/49*50

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1/1*2+1/2*3+1/3*4+…+1/49*501/1*2+1/2*3+1/3*4+…+1/49*501/1*2+1/2*3+1/3*4+…+1/49*501/1*2+1/2*3+1/3*4+…

1/1*2+1/2*3+1/3*4+…+1/49*50
1/1*2+1/2*3+1/3*4+…+1/49*50

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