tính $\frac{1}{3}$ $\frac{1}{3^2}$ + $\frac{1}{3^3}$ +…+ $\frac{1}{3^100}$

0 bình luận về “tính $\frac{1}{3}$ $\frac{1}{3^2}$ + $\frac{1}{3^3}$ +…+ $\frac{1}{3^100}$”

1. Đặt `A= 1/3 + 1/3^2 + 1/3^3 +…+1/3^100`

   `1/3A= 1/3( 1/3 + 1/3^2 + 1/3^3 +…+1/3^100)`

   `1/3A = 1/3^2 + 1/3^3 + 1/3^4 +…+1/3^101`

   `A- 1/3 A= 1/3 + 1/3^2 + 1/3^3 +…+1/3^100- 1/3^2 – 1/3^3- 1/3^4 -…-1/3^101`

   `2/3 A= 1/3 – 1/3^101`

   `A= (1/3 – 1/3^101) : 2/3`

   `A= (1/3 – 1/3^101) . 3/2`

   `A= 1/2 – 1/(3^100 .2)`

   Vậy `A= 1/2 – 1/(3^100 .2)`

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