Find the sum of all positive integers less than 1000 ending in 3 or 7.
3+7
+
10*sum(1 to 9)+9(3+7)
+
10*sum(10 to 99)+90(3+7)
To find the sum of all positive integers less than 1000 ending in 3 or 7, we can use the concept of arithmetic series.
Step 1: Determine the first term and common difference of the series.
Since we are looking for positive integers less than 1000 ending in 3 or 7, the first term would be 3, and the common difference would be 10 (which represents the difference between consecutive terms).
Step 2: Determine the last term of the series.
To find the last term, we need to find the largest positive integer less than 1000 ending in 3 or 7. Since the last digit can only be either 3 or 7, we can count in increments of 10 to find the largest number. Starting from 3 and adding 10 each time, we get the sequence: 3, 13, 23, 33, ..., 993. We can see that the last term is 993.
Step 3: Calculate the number of terms in the series.
To find the number of terms, we can use the formula: number of terms = (last term - first term) / common difference + 1.
In this case, the number of terms = (993 - 3) / 10 + 1 = 99 + 1 = 100.
Step 4: Calculate the sum of the series using the formula for the sum of an arithmetic series.
The formula for the sum of an arithmetic series is: sum = (number of terms / 2) * (first term + last term).
In this case, the sum = (100 / 2) * (3 + 993) = 50 * 996 = 49800.
Therefore, the sum of all positive integers less than 1000 ending in 3 or 7 is 49800.