tính a/b biết a=1/1.300+1/2.301+…+1/101.400 b=1/1.102+1/2.103+..+1/299.400

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1. Đáp án:

    101/299

   Giải thích các bước giải:

   Ta có: A=1/1.300+1/2.301+…+1/101.400

   →A=1/299.(299/1.300+299/2.301+…+299/101.400)

   →A=1/299. ( 1+1/300+1/2-1/301+….+1/101-1/400)

   →A= 1/299.(1+1/2+….+1/101)-(1/300+1/301+….+1/400)

   Ta có: b=1/1.102+1/2.103+..+1/299.400

   → B= 1/101.(101/1.102+101/2.103+..+101/299.400)

   → B= 1/101 .(1+1/2+….+1/299) – (1/102+1/103+….+1/400)

   → B= (1+1/2+….+1/299)- (1/300+1/301+….+1/400)

   →A=1/299.(1+1/2+….+1/101)-(1/300+1/301+….+1/400)

   phần

   b=1/101.(1+1/2+….+1/101)-(1/300+1/301+….+1/400)

   →A/B=1/299:1/101

   →A/B=101/299

   vậy A/B=101/299

    

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2. Đáp án:

    

   Giải thích các bước giải:

   Ta có: a=1/1.300+1/2.301+…+1/101.400

   ⇒ a= 1/299.(299/1.300+299/2.301+…+299/101.400)

   ⇒ a= 1/299. ( 1+1/300+1/2-1/301+….+1/101-1/400)

   ⇒ a= 1/299.|(1+1/2+….+1/101)-(1/300+1/301+….+1/400)|

   Ta có: b=1/1.102+1/2.103+..+1/299.400

   ⇒ b= 1/101.(101/1.102+101/2.103+..+101/299.400)

   ⇒ 1/101.|(1-1/102+1/2-1/102+……+1/299-1/400)|

   ⇒ b= 1/101 .|(1+1/2+….+1/299) – (1/102+1/103+….+1/400)|

   ⇒ b= |(1+1/2+….+1/299)- (1/300+1/301+….+1/400)|

   ⇒a=1/299.|(1+1/2+….+1/101)-(1/300+1/301+….+1/400)|

   phần

   b=1/101.|(1+1/2+….+1/101)-(1/300+1/301+….+1/400)| 

   ⇒a/b=1/299:1/101

   ⇒a/b=101/299

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