`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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