The first n terms and Sn of sequence 3 / 2,5 / 4,9 / 8,17 / 16, ·· (2 ^ n) + 1 / 2 ^ n It seems that we are going to use some kind of dislocation subtraction

The first n terms and Sn of sequence 3 / 2,5 / 4,9 / 8,17 / 16, ·· (2 ^ n) + 1 / 2 ^ n It seems that we are going to use some kind of dislocation subtraction

3/2=1+1/2
5/4=1+1/4
...
(2^n+1)/2^n=1+1/2^n
So Sn = n + 1 / 2 + 1 / 4 + 1 / 8 +... + 1 / 2 ^ n
After that is the equal ratio sequence
----------------------------------------------
Just use the sum formula of the equal ratio sequence
Sn=n+1-1/2^n