12+13+23+14+24+34+…+160+260+…+5960.
问题描述:
+1 2
+1 3
+2 3
+1 4
+2 4
+…+3 4
+1 60
+…+2 60
. 59 60
答
+1 2
+1 3
+2 3
+1 4
+2 4
+…+3 4
+1 60
+…+2 60
,59 60
=
+(1 2
+1 3
)+(2 3
+1 4
+2 4
)+…+(3 4
+1 60
+…+2 60
)59 60
=
+1+1 2
+…+3 2
59 2
=
+1 2
+2 2
+…+3 2
59 2
=(1+2+3+4+…+59)÷2
=(1+59)×59÷2÷2
=60×59÷4
=59×15
=885.
答案解析:先把分母相同的分数分为一组,通过计算或变形,把每个括号的结果写成分母是2的分数,运用用公式进行计算.
考试点:分数的巧算.
知识点:进行合理分组,运用公式,简便计算.