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Question Number 153006 by GalaxyBills last updated on 04/Sep/21

prove that 4!!=8 please help

$${prove}\:{that}\: \\ $$$$\mathrm{4}!!=\mathrm{8} \\ $$$${please}\:{help} \\ $$

Commented by talminator2856791 last updated on 04/Sep/21

that is wrong. n! = n∙(n−1)∙(n−2)∙.....∙2∙1 n!! = n!∙(n!−1)∙(n!−2)∙.....∙ (n!−n)∙(n!−n−1)∙.....∙ (n!−2n)∙(n!−2n−1)∙.....∙ ..................................... . . n∙(n−1)∙.....∙2∙1 4!! = 4!∙(4!−1)∙.....∙2∙1 =24∙23∙.....∙2∙1 = 620 448 401 733 239 439 360 000

$$\: \\ $$$$\:\mathrm{that}\:\mathrm{is}\:\mathrm{wrong}. \\ $$$$\: \\ $$$$\:{n}!\:=\:{n}\centerdot\left({n}−\mathrm{1}\right)\centerdot\left({n}−\mathrm{2}\right)\centerdot.....\centerdot\mathrm{2}\centerdot\mathrm{1} \\ $$$$\: \\ $$$$\:{n}!!\:=\:{n}!\centerdot\left({n}!−\mathrm{1}\right)\centerdot\left({n}!−\mathrm{2}\right)\centerdot.....\centerdot \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\left({n}!−{n}\right)\centerdot\left({n}!−{n}−\mathrm{1}\right)\centerdot.....\centerdot \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\left({n}!−\mathrm{2}{n}\right)\centerdot\left({n}!−\mathrm{2}{n}−\mathrm{1}\right)\centerdot.....\centerdot \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:..................................... \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{n}\centerdot\left({n}−\mathrm{1}\right)\centerdot.....\centerdot\mathrm{2}\centerdot\mathrm{1} \\ $$$$\:\: \\ $$$$\:\mathrm{4}!!\:=\:\mathrm{4}!\centerdot\left(\mathrm{4}!−\mathrm{1}\right)\centerdot.....\centerdot\mathrm{2}\centerdot\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:=\mathrm{24}\centerdot\mathrm{23}\centerdot.....\centerdot\mathrm{2}\centerdot\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:=\:\mathrm{620}\:\mathrm{448}\:\mathrm{401}\:\mathrm{733}\:\mathrm{239}\:\mathrm{439}\:\mathrm{360}\:\mathrm{000} \\ $$$$\: \\ $$

Commented by mr W last updated on 04/Sep/21

n!!≠(n!)! n!!=n×(n−2)×(n−4)×...×2 or 1

$${n}!!\neq\left({n}!\right)! \\ $$$${n}!!={n}×\left({n}−\mathrm{2}\right)×\left({n}−\mathrm{4}\right)×...×\mathrm{2}\:{or}\:\mathrm{1} \\ $$

Commented by mr W last updated on 04/Sep/21

there is no why, just know it if you didn′t already know.

$${there}\:{is}\:{no}\:{why},\:{just}\:{know}\:{it}\:{if}\:{you} \\ $$$${didn}'{t}\:{already}\:{know}. \\ $$

Commented by talminator2856791 last updated on 04/Sep/21

why?

$$\:\mathrm{why}? \\ $$

Commented by talminator2856791 last updated on 04/Sep/21

then what is n!!!?

$$\:\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:{n}!!!? \\ $$

Commented by mr W last updated on 04/Sep/21

Commented by mr W last updated on 04/Sep/21

n!!!=n(n−3)(n−6)...

$${n}!!!={n}\left({n}−\mathrm{3}\right)\left({n}−\mathrm{6}\right)... \\ $$

Commented by Rasheed.Sindhi last updated on 04/Sep/21

If mod(n,3)=1: n!!!=n(n−3)(n−6)...×7×4×1 If mod(n,3)=2: n!!!=n(n−3)(n−6)...×8×5×2 If mod(n,3)=0: n!!!=n(n−3)(n−6)...×9×6×3

$${If}\:{mod}\left({n},\mathrm{3}\right)=\mathrm{1}: \\ $$$${n}!!!={n}\left({n}−\mathrm{3}\right)\left({n}−\mathrm{6}\right)...×\mathrm{7}×\mathrm{4}×\mathrm{1} \\ $$$${If}\:\:{mod}\left({n},\mathrm{3}\right)=\mathrm{2}: \\ $$$${n}!!!={n}\left({n}−\mathrm{3}\right)\left({n}−\mathrm{6}\right)...×\mathrm{8}×\mathrm{5}×\mathrm{2} \\ $$$${If}\:{mod}\left({n},\mathrm{3}\right)=\mathrm{0}: \\ $$$${n}!!!={n}\left({n}−\mathrm{3}\right)\left({n}−\mathrm{6}\right)...×\mathrm{9}×\mathrm{6}×\mathrm{3} \\ $$

Answered by puissant last updated on 04/Sep/21

n!!=n(n−2)(n−4)....×4×2 4!!=4×2=8.

$${n}!!={n}\left({n}−\mathrm{2}\right)\left({n}−\mathrm{4}\right)....×\mathrm{4}×\mathrm{2} \\ $$$$\mathrm{4}!!=\mathrm{4}×\mathrm{2}=\mathrm{8}. \\ $$

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