人教版六年级数学寒假作业巧算题(1)1+1/2+1/4+1/8+1/16+1/32(2)3/10-3/100-3/1000……-3/1000000请写出过程,不要直接写答案,O(∩∩)O谢谢

Question

人教版六年级数学寒假作业巧算题
(1)1+1/2+1/4+1/8+1/16+1/32
(2)3/10-3/100-3/1000……-3/1000000
请写出过程,不要直接写答案,O(∩_∩)O谢谢

Answer 1

1+1/2+1/4+1/8+1/16+1/32 +1/32-1/32
=1+1/2+1/4+1/8+1/16+1/16-1/32
=1+1/2+1/4+1/8+1/8-1/32
=1+1/2+1/4+1/4-1/32
=1+1/2+1/2-1/32
=1+1-1/32
=63/32
原式=6/10-(3/10+3/100+3/1000+···+3/1000000)
=6/10-(3/10) * (1-1/1000000)/(1-1/10)
=0.6-0.333333
=0.266667
其中括号里为等比数列求和,应用求和公式