# Math Help - Proof sequence

1. ## Proof sequence

Can you help for this question ?

2. So: $a_1= 1$ and then $a_n= 2a_{\lfloor n/2\rfloor}$

Start by calculating values until you see a pattern:

For n= 2, n/2= 1 and so $a_2= 2a_1= 2$

For n= 3, n/2= 1.5 so $a_3= 2a_1= 2$

For n= 4, n/2= 2 so $n_4= 2a_2= 4$

For n= 5, n/2= 2.5 so $n_5= 2a_2= 4$

For n= 6, n/2= 3 so $n_6= 2a_3= 4$

For n= 7, n/2= 3.5 so $n_7= 2a_3= 4$

For n= 8, n/2= 4 so $n_8= 2a_4= 8$

Conjecture: if n is a power of 2 then $a_n= n$. If $2^k< n< 2^{k+1}$ then $a_n= 2^k< n$.