Prove by induction summation with exp index

Question

Hello I am new with induction and I am stuck on this summation

$\sum_{i=1}^{2^n} \frac{1}{(2i-1)} > \frac{n+3}{4}$

The $2^n$ confuses me

Any help would be appreciated. Thanks

Answer 1

You are adding up terms from $1$ to $2^n$

For the induction when you change n to n+1 you will have new terns from $2^n+1$ all the way up to $2^{n+1}$