The sum of all positive odd integers from 1 to 1000 is 250,000.
Calculating the Sum
Here's how to arrive at that answer:
-
Identify the Sequence: The sequence consists of the odd numbers 1, 3, 5, ..., 999.
-
Recognize the Arithmetic Progression: This is an arithmetic progression with a common difference of 2.
-
Determine the Number of Terms: The odd numbers between 1 and 1000 (inclusive) are half the numbers between 1 and 1000. Therefore, there are 1000/2 = 500 terms.
-
Apply the Formula for the Sum of an Arithmetic Series: The sum (S) of an arithmetic series is given by:
S = (n/2) * (first term + last term)
Where:
- n = number of terms
- first term = 1
- last term = 999
-
Calculate the Sum:
S = (500/2) (1 + 999)
S = 250 1000
S = 250,000
