1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55+1/66+1/78+1/91
问题描述：
1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55+1/66+1/78+1/91
答
原式=2/(2×3)+2/(3×4)+2/(4×5)+2/(5×6)+……+2/(13×14)
=2(1/2-1/3+1/3-1/4+1/4-1/5+……+1/13-1/14)
=2×(1/2-1/14)
=6/7
答
1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55+1/66+1/78+1/91
=6/7
答
设原式的和为S,再把原式乘以1/2得：
1/2S=1/2*（1/3+1/6+1/10+1/15+……+1/78+1/91）
1/2S=1/6+1/12+1/20+1/30+1/42+……+1/156+1/182
1/2S=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+……+1/12-1/13+1/13-1/14
1/2S=1/2-1/14
1/2S=6/14
两边乘以2得：S=6/7
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