a) To find the sum of the numbers from 1 to 2008, we can use the formula for the sum of an arithmetic series:

S = (n/2)(a + l)

where S is the sum, n is the number of terms, a is the first term, and l is the last term.

In this case, n = 2008, a = 1, and l = 2008. Plugging these values into the formula, we get:

A = (2008/2)(1 + 2008)
A = 1004(2009)
A = 2,018,036

Therefore, A = 2,018,036.

b) To find the sum of the odd numbers from 1 to 2007, we can use the formula for the sum of an arithmetic series:

S = (n/2)(a + l)

In this case, n = 1004 (since there are 1004 odd numbers from 1 to 2007), a = 1, and l = 2007. Plugging these values into the formula, we get:

B = (1004/2)(1 + 2007)
B = 502(2008)
B = 1,006,016

Therefore, B = 1,006,016.

c) To find the sum of the even numbers from 2 to 2008, we can use the formula for the sum of an arithmetic series:

S = (n/2)(a + l)

In this case, n = 1004 (since there are 1004 even numbers from 2 to 2008), a = 2, and l = 2008. Plugging these values into the formula, we get:

C = (1004/2)(2 + 2008)
C = 502(2010)
C = 1,010,020

Therefore, C = 1,010,020.

d) To find the sum of the squares of the numbers from 1 to 100, we can use the formula for the sum of the squares of an arithmetic series:

S = (n/6)(2n + 1)(n + 1)

In this case, n = 10 (since there are 10 terms from 1 to 100), so plugging this value into the formula, we get:

D = (10/6)(2(10) + 1)(10 + 1)
D = (10/6)(21)(11)
D = (10/6)(231)
D = 385

Therefore, D = 385.