What is the sum of the first 60 positive integers?
The famous mathematician Gauss, while he was in elementary school, notices the following
1+2+3+..+58+59+60
= (1+60) + (2+59) + (3+58) +.. (for a total of 30 of these pairs)
= 30(61)
= 1830
To find the sum of the first 60 positive integers, you can use a formula or a simple calculation.
One way to find the sum is to use the formula for the sum of an arithmetic series. The formula is:
Sum = (n/2) * (first term + last term)
In this case, the first term is 1 and the last term is 60. So, we can substitute these values into the formula:
Sum = (60/2) * (1 + 60)
= 30 * 61
= 1830
Therefore, the sum of the first 60 positive integers is 1830.
Alternatively, you can also calculate the sum by adding all the numbers together. Since the numbers start from 1 and go up to 60, you can use the formula for the sum of an arithmetic sequence:
Sum = (n/2) * (2a + (n-1)d)
In this case, n is 60, a is 1 (the first term), and d is 1 (the common difference). So, we can substitute these values into the formula:
Sum = (60/2) * (2(1) + (60-1)(1))
= 30 * (2 + 59)
= 30 * 61
= 1830
As a result, the sum of the first 60 positive integers is 1830.