Help with a couple Logic problems.

[Tsugytso]

Both questions Ask that I "list the first 10 terms of each of these sequences"

 

 

Question 1)

The sequence whose nth term is the largest integer whose binary expansion has n bits

 

I found two answers for this one, and they are as follows:

{1, 3, 7, 15, 31, 63, 127, 255, 511, 1023}

{1, 2, 4, 8, 16, 32, 64, 128, 256, 512}

 

I understand binary expansion as 2^n so the second makes sense (except I wouldn't do 2^0 and would end the sequence with 1024).

I'm guessing that the 'largest integer' part of this problem is throwing me off since I don't see how it alters the question rather than just saying 'integer.'

I'm just looking for an explanation I suppose.

 

Question 2)

The sequence whose nth term is the largest integer k such that k!

 

I've found the answer as:

{1; 2; 2; 2; 2; 3; 3; 3; 3; 3}

but not sure how this answer is obtained. help would be appreciated.

 

And for future reference, do I need to make a separate thread for each question from now on? And is this the right place for both of these questions?

[800]

not a GMAT question. is it ? out of scope.