1067-249-1067-250-

Question Number 183301 by sciencestudent last updated on 24/Dec/22

$$\begin{pmatrix}{\mathrm{1067}}\\{\mathrm{249}}\end{pmatrix}+\begin{pmatrix}{\mathrm{1067}}\\{\mathrm{250}}\end{pmatrix}=? \\ $$

Commented by JDamian last updated on 24/Dec/22

https://en.m.wikipedia.org/wiki/Pascal%27s_triangle

Commented by sciencestudent last updated on 25/Dec/22

$$? \\ $$

Commented by mr W last updated on 25/Dec/22

$${it}\:{can}\:{be}\:{easily}\:{shown}\:{that} \\ $$$$\begin{pmatrix}{{n}}\\{{k}−\mathrm{1}}\end{pmatrix}\:+\begin{pmatrix}{{n}}\\{{k}}\end{pmatrix}\:=\begin{pmatrix}{{n}+\mathrm{1}}\\{{k}}\end{pmatrix} \\ $$$${therefore} \\ $$$$\begin{pmatrix}{\mathrm{1067}}\\{\mathrm{249}}\end{pmatrix}\:+\begin{pmatrix}{\mathrm{1067}}\\{\mathrm{250}}\end{pmatrix}\:=\begin{pmatrix}{\mathrm{1068}}\\{\mathrm{250}}\end{pmatrix} \\ $$

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