Consider the following series: 1,2,3,4,5,10,20,40....which starts as an arithmetic series?

Question

...but after the first five terms becomes a geometric series. Prove that any positive integer can be written as a sum of distinct numbers from the series.
I know how to do the base case

Answer 1

all the numbers from 1-9 can be formed from the 1st five terms.

All multiples of 10 can be formed from the geometric terms (basically just a scaled binary sequence).

With that, all the gaps between the tens can be filled with the units.

Answer 2

Hey steve, can you show how to solve that using strong induction?