Use Gauss's approach to find the follwing sums 1 + 2 + 3 + 4 + ...+1002
There are 501 pairs, each adding up to 1002+1 = 1003
So the sum is 501*1003 = _____
To find the sum of 1 + 2 + 3 + 4 + ... + 1002 using Gauss's approach, we can apply the formula for the sum of an arithmetic series.
The formula for the sum of an arithmetic series is given by:
Sum = (n/2)(first term + last term)
In this case, the first term, a, is 1, the last term, l, is 1002, and the number of terms, n, is 1002.
Using the formula, we can calculate the sum as follows:
Sum = (1002/2) * (1 + 1002)
= 501 * 1003
= 501,003
Therefore, the sum of 1 + 2 + 3 + 4 + ... + 1002 is 501,003.
To find the sum of consecutive numbers from 1 to 1002, we can use Gauss's approach which involves using a formula to calculate the sum rather than manually adding each number.
Gauss's formula for calculating the sum of consecutive numbers is:
Sum = (n/2) * (first number + last number)
In this case, the first number is 1 and the last number is 1002. So we have:
Sum = (1002/2) * (1 + 1002)
First, we need to find the value of (1002/2).
1002 divided by 2 is 501. So, we have:
Sum = 501 * (1 + 1002)
Next, we need to calculate (1 + 1002).
1 + 1002 equals 1003. So, our equation becomes:
Sum = 501 * 1003
Now, we can multiply 501 by 1003 to find the sum:
501 * 1003 equals 502,503
Therefore, the sum of consecutive numbers from 1 to 1002 is 502,503.