Question

Find the sum of the first $1000$ positive integers.

Answer 1

Here, we will use the formula of the sum of $n$ positive integers. Integers are the numbers which can be positive or negative but we have to take only positive integers as it is given as positive integers. So, by applying the formula we will get the sum of the first $1000$ positive integers.

Formula used:
Sum of $n$ positive integers $= \dfrac{{n\left( {n + 1} \right)}}{2}$ where, $n$ is the number of integers.

Complete step by step solution:
It is given in the question that we have to take only positive integers and find their sum.
Number of integers for sum, $n = 1000$
We know the formula for the sum of $n$ positive integers is equal to $\dfrac{{n\left( {n + 1} \right)}}{2}$. Therefore, we get
Sum of the first $1000$ positive integers $= \dfrac{{1000\left( {1000 + 1} \right)}}{2}$
Now we have to solve this by simple calculation, we get
Sum of the first $1000$ positive integers $= 500 \times 1001 = 500500$

Hence, the sum of the first $1000$ positive integers is $500500$.

Note:
We should know the formula of the sum of $n$ positive integers. Integers are the numbers which can be positive or negative but integers can never be in fractional form or decimal form. Natural numbers are the positive integer numbers.
We should also know that addition of two numbers is the process of combining two numbers to make a single number and subtraction is the process of finding the difference between the two numbers. Even numbers are any integer that can be divided exactly by 2 is an even number. The last digit is 0, 2, 4, 6 or 8. Odd numbers are the numbers that cannot be divided by two. They are integers and not fractions.