Câu hỏi của ngọc anh

Question

A=1+3+3³+3^4_+...+3¹⁰ biết 2.A+1=3ⁿ tìm số n

tâm hoàng · Accepted Answer

$A=1+3+3^2+...+3^{10}$

$\Rightarrow3A=3+3^2+3^3+...+3^{11}$

$\Rightarrow3A-A=\left(3+3^2+3^3+...+3^{11}\right)-\left(1+3+3^2+..+3^{10}\right)$

$\Rightarrow2A=3^{11}-1$

Có $2A+1=3^n$

$\Rightarrow3^{11}-1+1=3^n\Rightarrow n=11$

Câu trả lời:

$A=1+3+3^2+...+3^{10}$

$\Rightarrow3A=3+3^2+3^3+...+3^{11}$

$\Rightarrow3A-A=\left(3+3^2+3^3+...+3^{11}\right)-\left(1+3+3^2+..+3^{10}\right)$

$\Rightarrow2A=3^{11}-1$

Có $2A+1=3^n$

$\Rightarrow3^{11}-1+1=3^n\Rightarrow n=11$