Question

To prove: (1 + 2 + 4 + . . . + 2n) + 1 = 2n+1 , ?n = 0 by induction

Answer 1

prove: (1 + 2 + 4 + . . . + 2n) + 1 = 2n+1

testing:
if n = 1 , LS = (1) + 1 = 2
RS = 2(1) + 1 = 3 FAIL
if n=2 , LS = (1 + 2) + 1 = 4
RS = 2(2) + 1 = 5 , FAIL again

Hard to prove something which is not true

check your spelling or the wording of the question.
I don't know what " ?n = 0 " is suppose to mean