[tex]=\Big\{\Big[\Big(\frac{2}{3}\Big)\Up^{1010}\Big]\Up^2\cdot\Big(\frac{2}{3}\Big)\Up^{20}-\Big(\frac{2}{3}\Big)\Up^{2000}\Big\}\cdot\Big(\frac{2}{3}\Big)\Up^{4000}[/tex]
[tex]=\Big[\Big(\frac{2}{3}\Big)\Up^{2020}\cdot\Big(\frac{2}{3}\Big)\Up^{20}-\Big(\frac{2}{3}\Big)\Up^{2000}\Big]\cdot\Big(\frac{2}{3}\Big)\Up^{4000}[/tex]
[tex]=\Big[\Big(\frac{2}{3}\Big)\Up^{2040}-\Big(\frac{2}{3}\Big)\Up^{2000}\Big]\cdot\Big(\frac{2}{3}\Big)\Up^{4000}[/tex]
[tex]=\Big(\frac{2}{3}\Big)\Up^{6040}-\Big(\frac{2}{3}\Big)\Up^{6000}[/tex]
[tex]=\frac{2^{6040}}{3^{6040}}-\frac{2^{6000}}{3^{6000}}[/tex]
[tex]=\frac{2^{6040}}{3^{6040}}-\frac{2^{6000}\cdot3^{40}}{3^{6040}}[/tex]
[tex]=\frac{2^{6040}-2^{6000}\cdot3^{40}}{3^{6040}}[/tex]
[tex]=\frac{2^{6000}(2^{40}-3^{40})}{3^{6040}}[/tex]
Mai departe nu mai stiu
