2/1*2+2/2*3+2/3*4+.......+2/n(n+1)
=2[1-1/2+1/2-1/3+1/3-1/4+...+1/n-1/(n+1）]
=2[1-1/(n+1)]
=2*(n+1-1)/(n+1)
=2n/(n+1)
2/1*2+2/2*3+2/3*4+.......+2/n(n+1)
=2*(1/1*2+1/2*3+1/3*4+....+1/n(n+1))
=2*(1-1/2+1/2-1/3+1/3-1/4+......+1/n-1/(n-1))
=2*(1-1/(n-1))
=2*(n-1-1)/(n-1)
=2(n-2)/(n-1)
2n/(n+1)
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