2分之1+6分之1+12分之1+...+2450分之1=?

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2分之1+6分之1+12分之1+...+2450分之1=?

1/2+1/6+1/12+...+1/2450
=1/(1*2)+1/(2*3)+1/(3*4)+...+1/(49*50)
=(1-1/2)+(1/2-1/3)+...+(1/49-1/50)
=1-1/50
=49/50

1/2+1/6+1/12+...+1/2450
=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)
=1-1/50
=49/50