Câu hỏi của Đặng Kim Cương

Question

1)tính

2^100-(1+2+2^2+2^3+....+2^100)

Thuỳ Linh Nguyễn · Accepted Answer

Đặt $A=1+2+2^2+2^3+...+2^{100}\ 2A=2+2^2+2^3+2^4+...+2^{101}\ 2A-A=2+2^2+2^3+2^4+...+2^{101}-1-2-2^2-2^3-...-2^{100}\ A=2^{101}-1$

$\Rightarrow2^{100}-\left(2^{100}-1\right)=2^{100}-2^{101}+1$

Câu trả lời:

Đặt $A=1+2+2^2+2^3+...+2^{100}\ 2A=2+2^2+2^3+2^4+...+2^{101}\ 2A-A=2+2^2+2^3+2^4+...+2^{101}-1-2-2^2-2^3-...-2^{100}\ A=2^{101}-1$

$\Rightarrow2^{100}-\left(2^{100}-1\right)=2^{100}-2^{101}+1$