HKIMO 2020 Grade 6 National Final (Heat) Set 01 Question 8

Find $\frac 1{256}+\frac 1{128}+\frac 1{64}+\cdots+\frac 14+\frac 12+1+2+4+\cdots+64+128+256$. Write the answer as a mixed fraction.

Source glossary (English–Vietnamese): Value: giá trị; Mixed fraction: hỗn số.