1/6+1/12+1/20…+1/n(n+1)=

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1/6+1/12+1/20…+1/n(n+1)=1/6+1/12+1/20…+1/n(n+1)=1/6+1/12+1/20…+1/n(n+1)=1/6+1/12+1/20…+1/n(n+1)==1/2

1/6+1/12+1/20…+1/n(n+1)=
1/6+1/12+1/20…+1/n(n+1)=

1/6+1/12+1/20…+1/n(n+1)=
1/6+1/12+1/20…+1/n(n+1)=
=1/2×3+1/3×4+1/4×5+...+1/n(n+1)
=1/2-1/3+1/3-1/4+1/4-1/5+...+1/n-1/(n+1)
=1/2-1/(n+1)
=(n-1)/[2(n+1)]