What is the sum of the integers from 1 to 100?

• A. 5050
• B. 4900
• C. 5000
• D. 5100

Answer: (A)

To find the sum of the integers from 1 to 100, you can use the formula for the sum of an arithmetic series. The formula is given by:

[

S_n = \frac{n}{2} (a + l)

]

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

In this case, the first term ( a ) is 1, the last term ( l ) is 100, and the number of terms ( n ) is 100. Plugging these values into the formula:

[

S_{100} = \frac{100}{2} (1 + 100) = 50 \times 101 = 5050

]

This shows that the total sum of the integers from 1 to 100 is indeed 5050. It utilizes the fact that the series (1 to 100) forms a symmetrical structure where pairs of numbers from the ends add up to the same total (1 + 100, 2 + 99, and so on). Hence, the