Question

If (2000!)/(1000!) = k (1 x 3 x 5 x 7 ... 1997 x 1999). What is the value of k?

Answer 1

\[\frac{2000!}{1000!}=\frac{2000 \cdots \cdot 1001 \cdot 1000!}{1000!}=2000 \cdots 1001\]

so we have

\[2000 \cdots 1001 =k(1 \cdot 3 \cdot 5 \cdot 7 \cdots 1997 \cdot 1999)\]
\[k=\frac{2000 \cdots 1001}{1 \cdot 3 \cdots 1999}\]

Answer 2

I had trouble with simplifying.

Answer 3

k = (2 x 4 x 6 x 8 x... 1998 x 2000)/ (1000!)
(2(1 x 2 x 3 x 4 x... 999 x 1000)/ (1000!)

= (2(1000!)/(1000!) = 2

Answer 4

k = 2

Answer 5

Sorry, but that does not seem correct. The denominator is solely composed of odd numbers.

Answer 6

You know the answer?

Answer 7

No. That's why I'm asking ... but 2 cannot be correct.

Answer 8

2000! / (1 x 3 x 5 x 7 ... 1997 x 1999)

= 2 x 4 x 6 x 8 x ... 2000

Answer 9

It's not 2000!. The numbers only go down to 1001.

Answer 10

k should be 2^1000 i believe

Answer 11

@joemath 2 x 4 x 6 x 8 x ... 2000 = 2(1000!)

Answer 12

no, (2+4+6+...+2000)=2(1+2+...+1000), we are multiplying here.

Answer 13

joe is correct

Answer 14

Yeah sorry

Answer 15

I thought it was plus

Answer 16

I think Joe has the correct answer.

Answer 17

sorry joe i have to go
don't be mad

Answer 18

always leave when he comes on

Answer 19

lol

Answer 20

bye zarkon and everyone else

Answer 21

later

Answer 22

I think k = 2^1000
Mathematica solution is attached.

Answer 23

we already have a solution...Mathematica is not needed...the human mind triumphs again :)

Answer 24

Sorry. I was working on it and didn't notice the posting.