1/20+1/30+1/42+1/56+...+1/132 数学题

来源：百度知道 编辑：UC知道 时间：2024/06/06 00:03:54
用简便方法

1/20+1/30+1/42+1/56+...+1/132
=1/4*5+1/5*6+1/6*7+....+1/11*12
=1/4-1/5+1/5-1/6+1/6-1/7....+1/11-1/12
=1/4-1/12
=3/12-1/12
=2/12
=1/6

1/20+1/30+1/42+1/56+...+1/132
=1/(4*5)+1/(5*6)+1/(6*7)+...1/(11*12)
=(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+...+(1/11-1/12)
=1/4-1/12
=1/6

1/20+1/30+1/42+1/56+...+1/132
=(5-4)/(4*5)+(6-5)/(6*5)+.....+(12-11)/(12*11)
=1/4-1/5+1/5-1/6+.....1/11-1/12
=1/4-1/12
=1/6

这种问题，一般都是把各个数拆开，然后通过前后项的消除，最后得到结果1/20+1/30+1/42+1/56+...+1/132
=1/4*5+1/5*6+1/6*7+....+1/11*12
=1/4-1/5+1/5-1/6+1/6-1/7....+1/11-1/12
=1/4-1/12
=3/12-1/12
=2/12
=1/6

1/4-1/5+1/5-1/6+...+1/11-1/12
=1/4-1/12
=1/6