Question

tính giá trị của các biểu thức sau

\(C=1-2+2^2-2^3+...-2^{2011}+2^{2012}\)

\(D=-2+2^2-2^3+2^4-...-2^{2019}+2^{2020}\)

Answer 1

\(C=1-2+2^2-2^3+...-2^{2011}+2^{2012}\)

\(\Rightarrow2C=2-2^2+2^3-2^4+...-2^{2012}+2^{2013}\)

\(\Rightarrow3C=1+2^{2013}\)

\(\Rightarrow C=\frac{1+2^{2013}}{3}\)

Vậy 

Answer 2

\(D=-2+2^2-2^3+2^4-...-2^{2019}+2^{2020}\)

\(\Rightarrow-2D=2^2-2^3+2^4-2^5+...+2^{2020}-2^{2021}\)

\(\Rightarrow-3D=-2^{2021}+2\)

\(\Leftrightarrow D=\frac{2^{2021}-2}{3}\)

Answer 3

D \(=-2+2^2-2^3+2^4-...-2^{2019}+2^{2020}\)

\(\Leftrightarrow2D=-2^2+2^3-2^4+2^5-...-2^{2020}+2^{2021}\)

\(\Leftrightarrow2D+D=2^{2021}-2\)

\(\Leftrightarrow3D=2^{2021}-2\)

\(\Leftrightarrow D=\frac{2^{2021}-2}{3}\)

Vậy \(D=\frac{2^{2021}-2}{3}\)

@@ Học tốt