Simplify. `1 / (n!) - 1 / ((n - 1)!) - 1 / ((n -2)!)`

Simplify. 1 / (n!) - 3 / ((n + 1)!) - (n^2 -4) / ((n + 2)!)

Simplify. 1 / ((n - 1) !) + (1 - n) / ((n + 1)!)

Simplify. (n + 2) / (n!) - (3n + 1) / ((n + 1)!)

Simplify. n[n! + (n - 1)!] + n^2 (n - 1)! + (n + 1)!

Simplify. ((2n + 2)!) / (2n!)

Simplify. ((n + 3)!) / ((n^2 - 4) (n +1)!)

Find n if. (n + 1)! = 42 xx (n - 1)!

Show that : (n !) / (r ! (n - r) !) + (n !) / ((r - 1) ! (n - r + 1) !) = ((n + 1) !) / (r ! (n - r +1) !)

Find n if. (((2n) !) / (7 !(2n - 7) !)) / ((n !) / (4 !(n - 4) !)) = 24 / 1

Find the sum of 1^1 n + 2^2 (n - 1) + 3^2 (n - 2) + 4^2 (n -3) ……upto 'n' terms.