The sum of the first \(2n\) terms of \[1,1,2,\frac{1}{2},4,\frac{1}{4},8,\frac{1}{8},16,\frac{1}{16},..\] is

\(2^n+1-2^{1-n}\),

\(2^n+2^{-n}\),

\(2^{2n}-2^{3-2n}\),

\(\frac{2^n-2^{-n}}{3}\).

Could we separate the sequence into two sub-sequences?

What kind of sequences do we have here?

Do we know a formula that helps us sum these sequences?