30. Quickly now, what is the sum of all integers from 1 to 100?.

5050

Step-by-step explanation:

Natural numbers from 1 to 100 is a set of the first 100 natural numbers, with 1 as the natural number and 100 as the largest one. Natural numbers being part of the number system includes all the positive integers from 1 to infinity. These are also called counting numbers as they do not include zero or negative numbers. The set of natural numbers is a classification under the bigger set of real numbers including only the positive integers, but not zero, fractions, decimals, and negative numbers.

The natural numbers from 1 to 100 can be written as 1, 2, 3, 4,5…….100 is an arithmetic progression (A.P). The sum of all natural numbers 1 to 100 can be calculated using the formula, S= n/2[2a + (n − 1) × d], where n is the total number of natural numbers from 1 to 100, d is the difference between the two consecutive terms, and a is the first term. There are a total of 100 natural numbers, so n = 100.

Thus, a = 1, d = 1 and n = 100

Let's calculate the sum of the natural numbers 1 to 100

The sum of an A.P,

S = n/2[2a + (n − 1) × d]

S = 100/2[2 + (100 – 1) × 1]

S = 50 [2 + 99]

S = 5050

Therefore, the sum of natural numbers from 1 to 100 is 5050.