Review question

# Can we sum the first $2n$ terms of $1,1,2,\frac{1}{2},4,\frac{1}{4},8,\frac{1}{8},..$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6257

## Suggestion

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

1. $2^n+1-2^{1-n}$,

2. $2^n+2^{-n}$,

3. $2^{2n}-2^{3-2n}$,

4. $\frac{2^n-2^{-n}}{3}$.

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?