计算:1/2+1/6+1/12+...+1/10100
问题描述：
计算:1/2+1/6+1/12+...+1/10100
答
1/2+1/6+1/12+...+1/10100
=1/(1×2)+1/(2×3)+1/(3×4)+.+1/(100×101)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/100-1/101)
=1-1/2+1/2-1/3+.+1/100-1/101
=1-1/101
=100/101;
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