P= $\frac{1}{100}$ – $\frac{1}{100×99}$ – $\frac{1}{99×98}$ – … – $\frac{1}{3×2}$ – $\frac{1}{2×1}$

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1. `P = 1/100 – 1/(100.99) – 1/(99.98) – …..- 1/(3.2) – 1/(2.1)`

   `= 1/100 – (1/(100.99) + 1/(99.98)+ …..- 1/(3.2)+ 1/(2.1))`

   `= 1/100 – (1/(1.2) + 1/(2.3) + ….+ 1/(98.99) + 1/(99.100))`

   `= 1/100 – (1 – 1/2 + 1/2 – 1/3+….+1/98-1/99+1/99-1/100)`

   `= 1/100 – (1 – 1/100) `

   `= 1/100 – 99/100`

   `= -98/100`

   `= -49/50`

   (Chúc bạn học tốt)

    

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2. `P = 1/100 – 1/(100.99) – 1/(99.98) – … – 1/(3.2) – 1/(2.1)`

   `P = 1/100 – (1/(100.99) + 1/(99.98) + …. + 1/(3.2) + 1/(2.1))`

   Đặt:

   `A = 1/(100.99) + 1/(99.98) + …. + 1/(3.2) + 1/(2.1)`

   `A = 1/(1.2) + 1/(2.3) + …. + 1/(98.99) + 1/(99.100)`

   `A = 1 – 1/2 + 1/2 – 1/3 + 1/3 – …. + 1/99 – 1/100`

   `A = 1 – 1/100`

   `A = 99/100`

   `=> P = 1/100 – (1/(100.99) + 1/(99.98) + …. + 1/(3.2) + 1/(2.1))`

   `P = 1/100 – 99/100`

   `P = (-49)/50`

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