1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7 简便运算怎么算?
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![1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7 简便运算怎么算?](/uploads/image/z/8620482-66-2.jpg?t=1%2F1%2A2%2B1%2F2%2A3%2B1%2F3%2A4%2B1%2F4%2A5%2B1%2F5%2A6%2B1%2F6%2A7+%E7%AE%80%E4%BE%BF%E8%BF%90%E7%AE%97%E6%80%8E%E4%B9%88%E7%AE%97%3F)
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1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7 简便运算怎么算?
1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7 简便运算怎么算?
1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7 简便运算怎么算?
1/m(m+1)=1/m-1/(m+1)
原式=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)
=1/1-1/2+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
1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)
=1-1/2+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
1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7
=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