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

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`