Tính tỉ số A/B biết: A= 1/1*2+1/3*4+1/5*6+…+1/199+200 B= 1/101*200+1/102*199+…+1/200*101

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1. `A = 1/1.2+ 1/3.4 + 1/5.6 + … + 1/199.200`

   `A = 1/1 – 1/2 + 1/3 – 1/4 + 1/5 – 1/6 + … + 1/199 – 1/200`

   `A = ( 1/1 + 1/3 + 1/5 + … + 1/199 ) – ( 1/2 + 1/4 + 1/6 + …+ 1/200 )`

   `A = ( 1/1 + 1/2+ 1/3 + 1/4 + 1/5 + … + 1/199 + 1/200 ) – 2. (1/2 + 1/4 + 1/6 + …+ 1/200 )`

   `A = 1/101 + 1/102 + … + 1/200 `

   `B = 1/101.200 + 1/102.199 + … + 1/200.101`

   `B` = `1/201`.( $\frac{101+200}{101.200}$ + $\frac{102+299}{102.199}$ + …+ $\frac{200+101}{200.101}$

   `B = 1/301 ( 1/200 + 1/101 + … + 1/101 + 1/200 )`

   `B = 1/301 . 2( 1/101 + 1/102 +…+ 1/200 )`

   `B = 2/301 ( 1/101 + 1/102 +…+1/200 )`

   ⇒ `A/B` = $\frac{\frac{1}{101} + \frac{1}{102} + … + \frac{1}{200}}{\frac{2}{301} ( \frac{1}{101} + \frac{1}{102} + … + \frac{1}{200})}$ 

   = `301/2`

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