Question

How much smaller is the sum of the first 1000 natural numbers than the sum of the first 1001 natural numbers?

Answer 1

ANSWER

1001

EXPLANATION

The sum of the first n - natural numbers is

$S_n= \frac{n}{2} (2a + d(n - 1))$

The sum of the first 1000 terms is

$S_{1000}= \frac{1000}{2} (2(1) + 1(1000 - 1))$

$S_{1000}=500 (1001)$

$S_{1000}=500500$

The sum of the first 1001 terms is

$S_{1001}= \frac{1001}{2} (2(1) + 1(1001 - 1))$

$S_{1001}= 1001 \times (501)$

$= 501501$

The difference is

$501501 - 500500= 1001$

Answer 2

The sum of the first 1000 natural numbers is 1001 smaller than the sum of the first 1001 natural numbers

How to determine the difference between the set of numbers?

The first 1000 natural numbers are 1 to 1000 while the first 1001 natural numbers are 1 to 1001

This means that:

The sum of the first 1001 natural numbers = 1001 + The sum of the first 1000 natural numbers

Rewrite as:

The sum of the first 1001 natural numbers - The sum of the first 1000 natural numbers = 1001

Hence, the sum of the first 1000 natural numbers is 1001 smaller than the sum of the first 1001 natural numbers

Read more about natural numbers at:

https://brainly.com/question/22250484