What are the odd integers between 1 and 2001?

The odd integers between 1 and 2001 are: 1, 3, 5, 7, ..., 1997, 1999, 2001.

These numbers form an arithmetic progression with a common difference of 2. To determine how many odd integers are in this sequence, we can use the formula for the nth term of an arithmetic sequence:

a_n = a₁ + (n - 1)d

where:

• a_n is the nth term (in this case, 2001)
• a₁ is the first term (in this case, 1)
• n is the number of terms (what we want to find)
• d is the common difference (in this case, 2)

So, we have:

2001 = 1 + (n - 1)2

Solving for n:

2000 = (n - 1)2
1000 = n - 1
n = 1001

Therefore, there are 1001 odd integers between 1 and 2001, and the complete list is:

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, ..., 1983, 1985, 1987, 1989, 1991, 1993, 1995, 1997, 1999, 2001