[math]A = \sum_{i=0}^{2022} \frac{x^{2^i}}{1-x^{2^{i+1}}}[/math]để ý: [math]A = \sum_{i=0}^{2022} \frac{1+x^{2^i}-1}{(1+x^{2^i})(1-x^{2^i})} = \sum_{i=0}^{2022} \frac{1}{1-x^{2^i}} - \frac 1 {1-x^{2^{i+1}}}[/math]vt lại: [math]A = \frac 1 {1-x} - \frac{1}{1-x^2} + \frac 1 {1-x^2} - \frac1{1-x^4}+..+\frac 1 {1-x^{2^n}}-\frac 1 {1-x^{2^{n+1}}} = \frac 1 {1-x} -\frac 1 {1-x^{2^{n+1}}}[/math]thay số thoi, [math]A = \frac 1 {1- \sqrt[2^{2022}]{2}}+1[/math]
