Numerical estimation
$begingroup$
Show that the numerical value of the expression
$frac{2times4times6timesdotstimes2020}{1times3times5timesdotstimes2019}$
is between 44 and 64.
number-theory estimation
asked Jan 6 at 18:56
Bob JohnsonBob Johnson
61
$endgroup$
add a comment |
$begingroup$
Show that the numerical value of the expression
$frac{2times4times6timesdotstimes2020}{1times3times5timesdotstimes2019}$
is between 44 and 64.
number-theory estimation
asked Jan 6 at 18:56
Bob JohnsonBob Johnson
61
$endgroup$
add a comment |
$begingroup$
Show that the numerical value of the expression
$frac{2times4times6timesdotstimes2020}{1times3times5timesdotstimes2019}$
is between 44 and 64.
number-theory estimation
asked Jan 6 at 18:56
Bob JohnsonBob Johnson
61
$endgroup$
Show that the numerical value of the expression
$frac{2times4times6timesdotstimes2020}{1times3times5timesdotstimes2019}$
is between 44 and 64.
number-theory estimation
number-theory estimation
asked Jan 6 at 18:56
Bob JohnsonBob Johnson
61
asked Jan 6 at 18:56
Bob JohnsonBob Johnson
61
asked Jan 6 at 18:56
Bob JohnsonBob Johnson
61
asked Jan 6 at 18:56
Bob JohnsonBob Johnson
61
asked Jan 6 at 18:56
Bob JohnsonBob Johnson
61
61
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Note that $$frac{2cdot4cdotldotscdot(2n)}{1cdot3cdotldotscdot(2n-1)}
=frac{2^{2n}(n!)^2}{(2n)!}$$
Then use the Stirling formula ($n=1010$)
$$
n! sim sqrt {2pi n} n^n e^{-n}
$$
answered Jan 6 at 19:17
Dietrich BurdeDietrich Burde
81.2k648106
$endgroup$
$begingroup$
Why did you invert the fraction?
$endgroup$
– EuxhenH
Jan 6 at 19:21
$begingroup$
@Cactus Because I had the formula for the inverted fraction at my hand - corrected (=inverted).
$endgroup$
– Dietrich Burde
Jan 6 at 20:06
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Note that $$frac{2cdot4cdotldotscdot(2n)}{1cdot3cdotldotscdot(2n-1)}
=frac{2^{2n}(n!)^2}{(2n)!}$$
Then use the Stirling formula ($n=1010$)
$$
n! sim sqrt {2pi n} n^n e^{-n}
$$
answered Jan 6 at 19:17
Dietrich BurdeDietrich Burde
81.2k648106
$endgroup$
$begingroup$
Why did you invert the fraction?
$endgroup$
– EuxhenH
Jan 6 at 19:21
$begingroup$
@Cactus Because I had the formula for the inverted fraction at my hand - corrected (=inverted).
$endgroup$
– Dietrich Burde
Jan 6 at 20:06
add a comment |
$begingroup$
Note that $$frac{2cdot4cdotldotscdot(2n)}{1cdot3cdotldotscdot(2n-1)}
=frac{2^{2n}(n!)^2}{(2n)!}$$
Then use the Stirling formula ($n=1010$)
$$
n! sim sqrt {2pi n} n^n e^{-n}
$$
answered Jan 6 at 19:17
Dietrich BurdeDietrich Burde
81.2k648106
$endgroup$
$begingroup$
Why did you invert the fraction?
$endgroup$
– EuxhenH
Jan 6 at 19:21
$begingroup$
@Cactus Because I had the formula for the inverted fraction at my hand - corrected (=inverted).
$endgroup$
– Dietrich Burde
Jan 6 at 20:06
add a comment |
$begingroup$
Note that $$frac{2cdot4cdotldotscdot(2n)}{1cdot3cdotldotscdot(2n-1)}
=frac{2^{2n}(n!)^2}{(2n)!}$$
Then use the Stirling formula ($n=1010$)
$$
n! sim sqrt {2pi n} n^n e^{-n}
$$
answered Jan 6 at 19:17
Dietrich BurdeDietrich Burde
81.2k648106
$endgroup$
Note that $$frac{2cdot4cdotldotscdot(2n)}{1cdot3cdotldotscdot(2n-1)}
=frac{2^{2n}(n!)^2}{(2n)!}$$
Then use the Stirling formula ($n=1010$)
$$
n! sim sqrt {2pi n} n^n e^{-n}
$$
answered Jan 6 at 19:17
Dietrich BurdeDietrich Burde
81.2k648106
edited Jan 6 at 19:29
answered Jan 6 at 19:17
Dietrich BurdeDietrich Burde
81.2k648106
answered Jan 6 at 19:17
Dietrich BurdeDietrich Burde
81.2k648106
answered Jan 6 at 19:17
Dietrich BurdeDietrich Burde
81.2k648106
81.2k648106
$begingroup$
Why did you invert the fraction?
$endgroup$
– EuxhenH
Jan 6 at 19:21
$begingroup$
@Cactus Because I had the formula for the inverted fraction at my hand - corrected (=inverted).
$endgroup$
– Dietrich Burde
Jan 6 at 20:06
add a comment |
$begingroup$
Why did you invert the fraction?
$endgroup$
– EuxhenH
Jan 6 at 19:21
$begingroup$
@Cactus Because I had the formula for the inverted fraction at my hand - corrected (=inverted).
$endgroup$
– Dietrich Burde
Jan 6 at 20:06
$begingroup$
Why did you invert the fraction?
$endgroup$
– EuxhenH
Jan 6 at 19:21
$begingroup$
Why did you invert the fraction?
$endgroup$
– EuxhenH
Jan 6 at 19:21
$begingroup$
@Cactus Because I had the formula for the inverted fraction at my hand - corrected (=inverted).
$endgroup$
– Dietrich Burde
Jan 6 at 20:06
$begingroup$
@Cactus Because I had the formula for the inverted fraction at my hand - corrected (=inverted).
$endgroup$
– Dietrich Burde
Jan 6 at 20:06
add a comment |
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