Câu hỏi của Trần Minh Nguyệt

Question

Rút Gọn 
A=2 mũ1+2 mũ2+2 mũ 3+...+2 mũ10
B=3 mux1+3 mũ 2+3 mũ 3+...+3 mũ 100

HT.Phong (9A5) · Accepted Answer

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

$\Rightarrow2A=2\cdot\left(2+2^2+2^3+...+2^{10}\right)$

$\Rightarrow2A=2^2+2^3+...+2^{11}$

$\Rightarrow2A-A=\left(2^2+2^3+...+2^{11}\right)-\left(2+2^2+...2^{10}\right)$

$\Rightarrow A=2^{11}-2$

$B=3^1+3^2+...+3^{100}$

$\Rightarrow3B=3\cdot\left(3+3^2+...+3^{100}\right)$

$\Rightarrow3B=3^2+3^3+...+3^{101}$

$\Rightarrow3B-B=\left(3^2+3^3+...+3^{101}\right)-\left(3+3^2+3^3+...+3^{100}\right)$

$\Rightarrow2B=3^{101}-3$

$\Rightarrow B=\dfrac{3^{101}-3}{2}$Câu trả lời: $A=2^1+2^2+2^3+...+2^{10}$