Question

Rut gon tong sau

C=1+2^2+2^4+....+2^2008

Answer 1

\(C=1+2^2+2^4+...+2^{2008}\)

\(4C=2^2+2^4+2^6+...+2^{2010}\)

\(4C-C=\left(2^2+2^4+2^6+...+2^{2010}\right)-\left(1+2^2+2^4+...+2^{2008}\right)\)

\(3C=2^{2010}-1\)

\(C=\frac{2^{2010}-1}{3}\)

Answer 2

\(C=1+2^2+2^4+...+2^{2008}\)

\(\Rightarrow4C=2^2+2^4+...+2^{2010}\)

\(\Rightarrow4C-C=\left(2^2+2^4+...+2^{2010}\right)-\left(1+2^2+2^4+...+2^{2008}\right)\)

\(\Rightarrow3C=2^{2010}-1\)

\(\Rightarrow C=\frac{2^{2010}-1}{3}\)