Question

Find r if , 2nCr=2nCr+2 ?

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Thus, The value of $r$ is $(n-1)$

Step-by-step explanation:

Find $r$ if  $_{r}^{2n}\textrm{C}=_{r+2}^{2n}\textrm{C}$

∴ $_{r}^{2n}\textrm{C}=_{r+2}^{2n}\textrm{C}$

⇒$\frac{(2n)!}{r!(2n-r)!} =\frac{(2n)!}{(r+2)!(2n-(r+2))!}$

⇒$\frac{(r+2)!}{r!} =\frac{(2n-r)!}{(2n-(r+2))!}$

⇒ $r+2=2n-r$

⇒$2r=2n-2$

⇒$r=\frac{2n-2}{2}$

∴ $r=n-1$

∴ The value of $r$ is $(n-1)$