计算1/2 +1/6+1/12+1/20+1/30+1/42=要简便计算

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计算1/2 +1/6+1/12+1/20+1/30+1/42=要简便计算
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计算1/2 +1/6+1/12+1/20+1/30+1/42=要简便计算
计算1/2 +1/6+1/12+1/20+1/30+1/42=
要简便计算

计算1/2 +1/6+1/12+1/20+1/30+1/42=要简便计算
1/2 +1/6+1/12+1/20+1/30+1/42
=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)
=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
(∵-1/2+1/2=0……抵消)
=1-1/7=6/7

用公式1/n(n+1)=1/n-(1/n+1)
所以原式=1/1x(1+1)+1/2x(2+1)+1/3x(3+1)+1/4x(4+1)+1/5x(5+1)+1/6x(6+1)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1-1/7
=6/7