1/2+1/3+2/3+1/4……+49/50

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

1/2+1/3+2/3+1/4……+49/50
1+2+3+……+(n-1)+n=(1+n)x(n/2)=n(n+1)/2
1+2+3+……+(n-2)+(n-1)=[1+(n-1)]x(n-1)/2=n(n-1)/2
1/n+2/n+.+(n-1)/n=[n(n-1)/2])/n=(n-1)/2
所以
1/2+1/3+2/3+1/4+2/4+3/4+1/5+2/5+…+1/50+2/50…+49/50
=(2-1)/2+(3-1)/2+.+(50-1)/2
=(1+2+3+.+49)/2
=[49x(49+1)/2]/2
=49x25/2
=612.5
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