Cho `A+1 – 3/4 + (3/4)^2 – (3/4)^3 + (3/4)^4 – (3/4)^5 – … – (3/4)^(2009) + (3/4)^(2010)`

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1. Đáp án:

    `đpcm`

   Giải thích các bước giải:

   `A=1-3/4+(3/4)^2-(3/4)^3+….-(3/4)^(2009)+(3/4)^(2010) `

   `=> A . 3/4=3/4-(3/4)^2+(3/4)^3+…-(3/4)^(2010)+(3/4)^(2011)`

   `=> 3/4 A+A=(3/4-(3/4)^2+(3/4)^3+…-(3/4)^(2010)+(3/4)^(2011))+(1-3/4+(3/4)^2-(3/4)^3+….-(3/4)^(2009)+(3/4)^(2010) )`

   `=>7/4A=(3/4)^(2011) + 1`

   `=> 7A=4. (3/4)^(2011) + 4`

   `=>` $\text{A không phải là số nguyên}$

   `=> đpcm` 

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