Đáp án+Giải thích các bước giải:

`color{#0A1433}{#}color{#142966}{ha}color{#1F3D99}{phu}color{#2E5CE6}{ongv}color{#5C85FF}{y0}color{#85A3FF}{1}color{#ADC2FF}{1}color{#C2D1FF}{2}`

Đặt `A=1 + 1/3^2 + 1/3^4 +...+1/3^100`

`1/3^2 A = 1/3^2 + 1/3^4 +1/3^6+...+1/3^102`

`A - 1/9 A = (1 + 1/3^2 + 1/3^4 +...+1/3^100) - (1/3^2 + 1/3^4 +1/3^6+...+1/3^102)`

`8/9 A = 1- 1/3^102`

`A = (3^102 - 1)/3 . 9/8 = [3(3^102 - 1)]/8 = (3^103 - 3)/8`

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