|1/2-1|+|1/3-1/2|+|1/4-1∕3|+………+|1∕100-1∕99|

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|1/2-1|+|1/3-1/2|+|1/4-1∕3|+………+|1∕100-1∕99|
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|1/2-1|+|1/3-1/2|+|1/4-1∕3|+………+|1∕100-1∕99|
|1/2-1|+|1/3-1/2|+|1/4-1∕3|+………+|1∕100-1∕99|

|1/2-1|+|1/3-1/2|+|1/4-1∕3|+………+|1∕100-1∕99|
可爱甜心苏菲儿
原式=1-1/2+1/2-1/3+1/3-1/4+……+1/99-1/100
=1-1/100
=99/100

|1/2-1|+|1/3-1/2|+|1/4-1∕3|+………+|1/100-1/99|
= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ………+1/99 - 1/100
= 1 - 1/100
= 99/100

│1/2-1│+│1/3-1/2│+│1/4-1/3│+...+│1/100-1/99│
=1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100
=1-1/100
=99/100 或=0.99