1, tính a,: 1/1.2 + 1/2.3 + 1/ 3.4 +.......+ 1/99. 100 b, 1/1.3 +1/3.5 + 1/5.7+.....+1/99.101

Câu `1` :
`a,` $\dfrac{1}{1 . 2}$ `+` $\dfrac{1}{2 . 3}$ `+` $\dfrac{1}{3 . 4}$ `+ ............ +` $\dfrac{1}{99 . 100}$

`=` `1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + .............. + 1/99 - 1/100`

`=` `1 - 1/100`

`=` `100/100 - 1/100`

`=` `99/100`


`b,` $\dfrac{1}{1 . 3}$ `+` $\dfrac{1}{3 . 5}$ `+` $\dfrac{1}{5 . 7}$ `+ .......... +` $\dfrac{1}{99 . 101}$

`=` `1/2 . ( 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ............. + 1/99 - 1/101 )`

`=` `1/2 . ( 1 - 1/101 )`

`=` `1/2 . 100/101`

`=` `50/101`


$\textit{#YN_Yuri}$

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