Asked by MO
Consider the following series: 1,2,3,4,5,10,20,40....which starts as an arithmetic series?
...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
...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
Answers
Answered by
Steve
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.
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.
Answered by
bcruga
Hey steve, can you show how to solve that using strong induction?