a) The sum of the first n natural numbers can be found using the formula: Sn = (n/2)(a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term. In this case, a = 1 and l = n. So, the sum of the first n natural numbers is Sn = (n/2)(1 + n).

b) The sum of the odd numbers from 1 to (2n + 1) can be found using the formula: Sn = (n/2)(a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term. In this case, a = 1 and l = (2n + 1). So, the sum of the odd numbers from 1 to (2n + 1) is Sn = (n/2)(1 + (2n + 1)).

c) The sum of an arithmetic series can be found using the formula: Sn = (n/2)(a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term. In this case, a = 2 and l = 2006. So, the sum of the arithmetic series 2, 5, 8, ..., 2006 is Sn = (n/2)(2 + 2006).

d) The sum of an arithmetic series can be found using the formula: Sn = (n/2)(a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term. In this case, a = 1 and l = 2005. So, the sum of the arithmetic series 1, 4, 7, ..., 2005 is Sn = (n/2)(1 + 2005).

e) The sum of an arithmetic series can be found using the formula: Sn = (n/2)(a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term. In this case, a = 2 and l = 2n. So, the sum of the arithmetic series 2, 4, 6, ..., 2n is Sn = (n/2)(2 + 2n).

g) The sum of an arithmetic series can be found using the formula: Sn = (n/2)(a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term. In this case, a = 1 and l = 2001. So, the sum of the arithmetic series 1, 5, 9, ..., 2001 is Sn = (n/2)(1 + 2001).