a) p = 1 + 9/45 + 9/105 + 9/189 + … + 9/29997

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1. Lời giải:

   $P=1+\dfrac{9}{45}+\dfrac{9}{105}+…+\dfrac{9}{29997}$

   $P=1+\dfrac{3}{15}+\dfrac{3}{45}+…+\dfrac{3}{9999}$

   $P=1+\dfrac{3}{3×5}+\dfrac{3}{5×7}+…+\dfrac{3}{99×101}$

   $P=\dfrac32\left(1-\dfrac13+\dfrac13-\dfrac15+…+\dfrac1{99}+\dfrac1{100}\right)$

   $P=\dfrac32\left(1-\dfrac1{100}\right)=\dfrac{150}{101}$

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2. P = 1 + `9/45` + `9/105` + `9/189` + … + `9/2997`

   P = 1 + `3/15` + `3/35` + `3/55` + …. + `3/9999`

   P = `3/1` x 3 + `3/3` x 5 + `3/5` x 7 + `3/11` x 5 + … + `3/99` x 101

   P = `3/2` x ( `2/1` x 3 + `2/3` x 5 + `2/5` x 7 + `2/11` x 5 + … + `2/99` x 101 )

   P = `3/2` x ( 1 – `1/3` + `1/3` – `1/5` + `1/5` – `1/7` + `1/7` – `1/11` + …. + `1/99` – `1/101` )

   P = `3/2` x ( 1 – `1/101` )

   P = `3/2` x `100/101`

   P = `150/101`

   `#cactus`

    

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