Question

Сравните 999!/998! и 1000!/999!

Answer 1

$\frac{999!}{998!}=999\\\\ \frac{1000!}{999!}=1000\\\\999\ \textless \ 1000 =\ \textgreater \ \frac{999!}{998!}\ \textless \ \frac{1000!}{999!}$

Answer 2

Comparison of 999!/998! and 1000!/999!

To compare the values of 999!/998! and 1000!/999!, let's first understand what these expressions represent.

The notation n! (read as "n factorial") represents the product of all positive integers from 1 to n. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

Now, let's calculate the values of 999!/998! and 1000!/999!:

- 999!/998!: - The numerator, 999!, represents the product of all positive integers from 1 to 999. - The denominator, 998!, represents the product of all positive integers from 1 to 998. - Since the denominator includes all the factors of the numerator, we can cancel out the common factors. - Therefore, 999!/998! simplifies to 999.

- 1000!/999!: - The numerator, 1000!, represents the product of all positive integers from 1 to 1000. - The denominator, 999!, represents the product of all positive integers from 1 to 999. - Again, since the denominator includes all the factors of the numerator, we can cancel out the common factors. - Therefore, 1000!/999! simplifies to 1000.

So, the comparison between 999!/998! and 1000!/999! is as follows:

999!/998! = 999

1000!/999! = 1000

Therefore, 999!/998! is equal to 999, while 1000!/999! is equal to 1000.

Please let me know if you need any further clarification or have any other questions!