To find the sum of an arithmetic sequence, we can use the formula:

Sum = (n/2)(first term + last term)

In this case, the first term is 1 and the last term is 2001. We need to find the number of terms, n, in the sequence.

The formula for the nth term of an arithmetic sequence is:

nth term = first term + (n-1) * common difference

In this case, the common difference is 2 (since we are dealing with odd integers).

To find the number of terms, we can rearrange the formula for the nth term:

n = (last term - first term + common difference) / common difference

n = (2001 - 1 + 2) / 2 n = 2002 / 2 n = 1001

Now we can substitute the values into the sum formula:

Sum = (n/2)(first term + last term) Sum = (1001/2)(1 + 2001) Sum = (1001/2)(2002) Sum = 1001 * 1001 Sum = 1,002,001

Therefore, the sum of the arithmetic sequence of odd integers from 1 to 2001 is 1,002,001.