Question

if (n+2)!=2550×n!
find n?

Answer 1

(n+2) (n+1) n! = 2550 × n!
(n+2) (n+1) = 2550
n^2 + 3n + 2 = 2550

Answer 2

AnswEr:

We have,

$\\ \qquad \tt \: (n + 2)! = 2550 \times n! \\ \\ \\ \implies \tt \: (n + 2)(n + 1) \times n! = 2550 \times n! \\ \\ \\ \implies \tt \: (n + 2) \times (n + 1) = 2550 \\ \\ \\ \implies \tt \: (n + 2)(n + 1) = 51 \times 50 \\ \\ \\ \implies \tt \: n + 2 = 51 \: \: or \: \: n + 1 = 50 \sf \qquad(by \: comparing) \\ \\ \\ \implies \tt \blue{n = 49}$

Hence, the value of n will be 49.