小学巧算题及答案1/2+1/6+1/12+1/20+1/30+...+1/9900

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小学巧算题及答案1/2+1/6+1/12+1/20+1/30+...+1/9900

小学巧算题及答案1/2+1/6+1/12+1/20+1/30+...+1/9900
小学巧算题及答案
1/2+1/6+1/12+1/20+1/30+...+1/9900

小学巧算题及答案1/2+1/6+1/12+1/20+1/30+...+1/9900
1/2+1/6+1/12+1/20+1/30+.+1/9900
=1/1×2+1/2×3+1/3×4+1/4×5+1/5×6+.+1/99×100
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+.+1/99-1/100
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+.+1/99-1/100
=1-1/100
=99/100