Question

2(\(\frac{n!}{\left(n-3\right)!}\)+3.\(\frac{n!}{\left(n-2\right)!}\))=(n+1)!

Answer 1

Ta có:

\(A=2\left(\frac{n!}{\left(n-3\right)!}+3.\frac{n!}{\left(n-2\right)!}\right)=2\left(\frac{n\left(n-1\right)\left(n-2\right)\left(n-3\right)!}{\left(n-3\right)!}+3.\frac{n\left(n-1\right)\left(n-2\right)!}{\left(n-2\right)!}\right)\)

\(=2\left[n\left(n-1\right)\left(n-2\right)+3n\left(n-1\right)\right]=2n\left(n-1\right)\left(n-2+3\right)=2n\left(n-1\right)\left(n+1\right)\)

Mà \(A=\left(n+1\right)!=\left(n+1\right)n\left(n-1\right)\left(n-2\right)!\)

\(\Rightarrow2=\left(n-2\right)!\Rightarrow n=4\)

 

Answer 2

Bài này là tìm n đúng không?