Câu hỏi của Truong Ducngoc

Question

tìm tổng dãy số trên

Nguyễn Hoàng Minh · Accepted Answer

$=5\left(1+2+4+8+...+256+512\right)\ =5\left(1+2+2^2+2^3+...+2^8+2^9\right)$

Đặt $A=1+2+2^2+...+2^9$

$\Rightarrow2A=2+2^2+2^3+...+2^{10}\ \Rightarrow2A-A=A=2^{10}-1\ \Rightarrow\text{Tổng }=5A=5\cdot2^{10}-5$

Câu trả lời:

$=5\left(1+2+4+8+...+256+512\right)\ =5\left(1+2+2^2+2^3+...+2^8+2^9\right)$

Đặt $A=1+2+2^2+...+2^9$

$\Rightarrow2A=2+2^2+2^3+...+2^{10}\ \Rightarrow2A-A=A=2^{10}-1\ \Rightarrow\text{Tổng }=5A=5\cdot2^{10}-5$