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计算：（1）(1/10-1/11)+(1/11-1/12)+(1/12-1/13)+.+(1/99-1/100)（2）1-1/2-1/4-1/8-1/16-1/32-1/64-1/128-1/256
题目详情
计算：
（1）(1/10-1/11)+(1/11-1/12)+(1/12-1/13)+.+(1/99-1/100)
（2）1-1/2-1/4-1/8-1/16-1/32-1/64-1/128-1/256
（1）(1/10-1/11)+(1/11-1/12)+(1/12-1/13)+.+(1/99-1/100)
（2）1-1/2-1/4-1/8-1/16-1/32-1/64-1/128-1/256
▼优质解答
答案和解析
(1/10-1/11)+(1/11-1/12)+(1/12-1/13)+.+(1/99-1/100)
=1/10+(-1/11+1/11)+(-1/12+1/12)+(-1/13+1/13)+.+(-1/99+1/99)-1/100
=1/10-1/100=9/100
1-1/2-1/4-1/8-1/16-1/32-1/64-1/128-1/256
=(1-1/2)-1/4-1/8-1/16-1/32-1/64-1/128-1/256
=1/2-1/4-1/8-1/16-1/32-1/64-1/128-1/256
=1/4-1/8-1/16-1/32-1/64-1/128-1/256
=1/8-1/16-1/32-1/64-1/128-1/256
=1/16-1/32-1/64-1/128-1/256
=1/32-1/64-1/128-1/256
=1/64-1/128-1/256
=1/128-1/256
=1/256
=1/10+(-1/11+1/11)+(-1/12+1/12)+(-1/13+1/13)+.+(-1/99+1/99)-1/100
=1/10-1/100=9/100
1-1/2-1/4-1/8-1/16-1/32-1/64-1/128-1/256
=(1-1/2)-1/4-1/8-1/16-1/32-1/64-1/128-1/256
=1/2-1/4-1/8-1/16-1/32-1/64-1/128-1/256
=1/4-1/8-1/16-1/32-1/64-1/128-1/256
=1/8-1/16-1/32-1/64-1/128-1/256
=1/16-1/32-1/64-1/128-1/256
=1/32-1/64-1/128-1/256
=1/64-1/128-1/256
=1/128-1/256
=1/256
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