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Question Number 71926 by TawaTawa last updated on 22/Oct/19

Commented by Prithwish sen last updated on 22/Oct/19

$$\mathbf{If}!!\mathbf{means}\mathbf{mere}\mathbf{factorial}\mathbf{than}3002!!\mathbf{must}$$$$\mathbf{be}\mathbf{divisible}\mathbf{by}2003$$$$\mathbf{i}.\mathbf{e}$$$$3092!!\equiv 0\left(\mathbf{mod}2003\right)$$

Commented by TawaTawa last updated on 23/Oct/19

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sirs}$$

Answered by MJS last updated on 22/Oct/19

$$\{\begin{array}{l}n=2k\Rightarrow n!!=2^{k}k!\\ n=2k-1\Rightarrow n!!=\frac{\left(2k\right)!}{2^{k}k!}\end{array}$$$$\mathrm{definition}:(-1)!!=0!!=1$$$$\Rightarrow$$$$3002!!=2^{1501}1501!$$

Commented by MJS last updated on 22/Oct/19

$$\mathrm{sorry}{\mathrm{it}}^{\prime }\mathrm{s}\mathrm{not}\mathrm{an}\mathrm{answer},\mathrm{just}\mathrm{an}\mathrm{explanation}$$

Commented by Prithwish sen last updated on 22/Oct/19

$$\mathrm{Thank}\mathrm{you}\mathrm{sir}.\mathrm{But}\mathrm{what}\mathrm{it}\mathrm{is}\mathrm{called}\mathrm{sir}?$$

Commented by MJS last updated on 22/Oct/19

$$‘‘\mathrm{double}{\mathrm{faculty}}^{″}$$$$n!!=n(n-2)(n-4)...$$

Commented by Prithwish sen last updated on 22/Oct/19

$$\mathrm{that}\mathrm{means}$$$$102!!=2.4.6.......102$$$$101!!=1.3.5......101$$$$102!=101!!.102!!$$$$\mathrm{Wow}!\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{sir}.\mathrm{I}\mathrm{learn}\mathrm{something}$$$$\mathrm{new}.$$

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