Question

rút gọn biểu thức :

G = \(\dfrac{1^{2010}+2^{2010}+3^{2010}+...+10^{2010}}{2^{2010}+4^{2010}+6^{2010}+...+20^{2010}}\)

Answer 1

\(C=\dfrac{1^{2010}+2^{2010}+3^{2010}+...+10^{2010}}{2^{2010}+4^{2010}+6^{2010}+...+20^{2010}}\)

\(=\dfrac{1^{2010}+2^{2010}+3^{2010}+...+10^{2010}}{1^{1010}.2^{2010}+2^{2010}.2^{2010}+2^{2010}.3^{2010}+...+2^{2010}.10^{2010}}\)

\(=\dfrac{1^{2010}+2^{2010}+3^{2010}+...+10^{2010}}{\left(1^{2010}+2^{2010}+3^{2010}+...+10^{2010}\right)+2^{2010}.2^{2010}.2^{2010}...2^{2010}}\)

\(=\dfrac{1}{2^{2010}+2^{2010}+2^{2010}+...+2^{2010}}\)

Answer 2

\(G=\dfrac{1^{2010}+2^{2010}+3^{2010}+...+10^{2010}}{2^{2010}+4^{2010}+....+20^{2010}}\\ =\dfrac{1^{2010}+2^{2010}+...+10^{2010}}{2^{2010}\left(1^{2010}+2^{2010}+...+10^{2010}\right)}\\ =\dfrac{1}{2^{2010}}\)

Answer 3

Theo bài ra, ta có:

\(G=\dfrac{1^{2010}+2^{2010}+3^{2010}+....+10^{2010}}{2^{2010}+4^{2010}+6^{2010}+....+20^{2010}}\)

\(\Rightarrow G=\dfrac{1^{2010}+2^{2010}+3^{2010}+....+10^{2010}}{2^{2010}\left(1^{1010}+2^{2010}+3^{2010}+....+10^{2010}\right)}\)

\(\Rightarrow G=\dfrac{1}{2^{2010}}\)

Vậy \(G=\dfrac{1}{2^{2010}}\)

Answer 4

\(G=\dfrac{1^{2010}+2^{2010}+3^{2010}+...+10^{2010}}{2^{2010}+4^{2010}+6^{2010}+...+20^{2010}}\)

Theo đề bài ra, ta có:

\(G=\dfrac{1^{2010}+2^{2010}+3^{2010}+...+10^{2010}}{2.\left(1^{2010}+2^{2010}+3^{2010}+...+10^{2010}\right)}\)

\(G=\dfrac{1}{2^{2010}}\)

Vậy...