Comparing Factorials and Exponentials: Which is Greater?

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In summary, to determine which is greater between two numbers, you can use the greater than (>) and less than (<) symbols. This applies to both numbers and variables, where you can assign values and compare them using the symbols. The difference between "greater than" and "greater than or equal to" is that the latter also returns true if the numbers are equal. There is no specific method for comparing fractions or decimals, but you can convert them to the same format and use the symbols. To compare a negative and positive number, you can use their absolute values and then compare them using the symbols.
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anemone
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Determine which of the following is greater?

$2015!$ or $1008^{2015}$?
 
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  • #2
anemone said:
Determine which of the following is greater?

$2015!$ or $1008^{2015}$?

we have
$1008^2 \gt (1008^2-n^2) \gt(1008-n)(1008+n)$
by taking n from 1007 to 1 we get
$1008^{2014}$ on LHS and $ 1 * 2 * \cdots 1007 * 2015 * \cdots * 1009 = \dfrac{2015!}{1008}$ on RHS
hence
$1008^{2014}\gt \dfrac{2015!}{1008} $
or $1008^{2015}\gt 2015! $
hence $1008^{2015}$ is greater
 
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  • #3
kaliprasad said:
we have
$1008^2 \gt (1008^2-n^2) \gt(1008-n)(1008+n)$
by taking n from 1007 to 1 we get
$1008^{2014}$ on LHS and $ 1 * 2 * \cdots 1007 * 2015 * \cdots * 1009 = \dfrac{2015!}{1008}$ on RHS
hence
$1008^{2014}\gt \dfrac{2015!}{1008} $
or $1008^{2015}\gt 2015! $
hence $1008^{2015}$ is greater

Very great job, kaliprasad!:cool:
 

FAQ: Comparing Factorials and Exponentials: Which is Greater?

How do you determine which is greater between two numbers?

To determine which is greater between two numbers, you can use the greater than (>) and less than (<) symbols. If the number on the left is greater than the number on the right, the statement will be true. If the number on the left is less than the number on the right, the statement will be false.

Can you determine which is greater between two variables?

Yes, you can determine which is greater between two variables by assigning values to the variables and then using the greater than (>) and less than (<) symbols to compare them. You can also use conditional statements or mathematical functions to compare the values of the variables.

What is the difference between "greater than" and "greater than or equal to"?

The "greater than" symbol (>) compares two numbers and returns true if the number on the left is greater than the number on the right. The "greater than or equal to" symbol (>=) also compares two numbers, but returns true if the number on the left is greater than or equal to the number on the right.

Is there a specific method for determining which is greater between fractions or decimals?

There is no specific method for determining which is greater between fractions or decimals. You can convert both to the same format (either fractions or decimals) and then use the greater than (>) or less than (<) symbols to compare them.

How can you determine which is greater between a negative and a positive number?

To determine which is greater between a negative and a positive number, you can use the absolute value of the numbers. The absolute value disregards the negative sign and gives the positive value of a number. You can then compare the absolute values using the greater than (>) or less than (<) symbols.

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