THAT statement is FALSE.
(2)(4)(6)(8) = 384
(2)(4)(4!) = 192
However if the right side of the equation was (2^k)(k!) then it would be right.
(2^4)(4!) = 384
(2)(4)(6)(8).... = (2)(1)(2)(2)(2)(3)(2)(4) .... = 2^k (1)(2)(3)(4) ... = (2^k)(k!)
Using math induction we can also show that the new equation is true.
If using k=1 the formula is true and ....(2k-4)(2k-2)(2k)(2k+2) = 2^(k+1)((k+1)!)
then for all k >= 1 ....(2k-4)(2k-2)(2k) = (2^k)(k!) must be true.
To show k=1 is true ... 2 = (2^1)(1!) -> 2=2 TRUE
To show ....(2k-4)(2k-2)(2k)(2k+2) = 2^(k+1)((k+1)!)
First take the original equation
....(2k-4)(2k-2)(2k) = (2^k)(k!)
Multiply by 2k+2 on each side
....(2k-4)(2k-2)(2k)(2k+2) = (2^k)(k!)(2k+2)
Now if we can make the left side into (2^(k+1))((k+1)!) then we've shown that the orginal equation is true.
.... = (2^k)(k!)2(k+1)
.... = 2(2^k)(k!)(k+1)
.... = (2^(k+1))(k!)(k+1)
.... = (2^(k+1))((k+1)!) YAH, OUR NEW EQUATION IS TRUE!
2006-07-09 20:57:26
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answer #1
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answered by Michael M 6
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True. Each factor in the expression (2)(4(6)(8) etc. is twice the size of the factors in a factorial (1)(2)(3)(4) etc. The number of factors is k, so we have k times 2 times the factorial, or (2k)(k1).
2006-07-09 20:25:44
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answer #2
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answered by Anonymous
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(2)(4)(6)(8)--- is part of (2k)(k!)
and so is (2k-4)(2k-2)(2k), because those are just the three numbers preceding 2k*k!.
Ex: (2k-2)=(2(k-1))
It's just a fancy way of writting it..., the (2k-4)(2k-2)(2k) would be included in the equation, regardless of wether or not they were stated, because if k=100, then they would be (196)(198)(200), and (2)(4)(6)(8)--- (196)(198)(200)=(2*100)(100!)
2006-07-09 21:03:11
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answer #3
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answered by Anonymous
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following michael m's reply
it should be (2^k)(k!)
if u factor a 2 out of every term of the LHS, u get:
(1*2)(2*2)(3*2)...{2(k-2)}{2(k-1)}(2k)
=(2*2*2*2*2...*2)(1*2*3*4*5...(k-2)(k-1)k)
=(2^k)(k!) by the definition of factorial
2006-07-10 01:27:01
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answer #4
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answered by angyansheng65537 2
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"That us of a(Iraq) will not be strong" With that truth on my own, this question will change into invalid because the best judgment behind the question became rooted on your previous statements. And someone's' answer had to be rooted behind your statements, yet, for this truth, you grant no sound good judgment or information. Iraq will be strong some day. And sure, our nationwide safe practices is at stake, thinking Al Qaeda is often in Iraq. And Osama considers it the important the front antagonistic to the west.
2016-11-06 03:19:54
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answer #5
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answered by ? 3
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that statement is never correct
probably on R.H.S side 2k must be replaced by 2 power k;
2006-07-09 22:03:01
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answer #6
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answered by ? 2
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true...lol
2006-07-09 20:20:14
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answer #7
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answered by Anonymous
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