The simplified expression of (20!+21!+22!)/44 is 20! * 11
How to simplify the expression?
The expression is given as:
(20!+21!+22!)/44
The factorial of a number n is:
n! = n * (n - 1)!
So, we start by expanding 22!
(20!+21!+22!)/44 = (20!+21!+22 * 21 * 20!)/44
Next, we expand 21!
(20!+21!+22!)/44 = (20!+21 * 20!+22 * 21 * 20!)/44
Factor out 20!
(20!+21!+22!)/44 = 20! * (1 + 21 + 22 * 21)/44
Evaluate the expression in the bracket
(20!+21!+22!)/44 = 20! * 484/44
Divide
(20!+21!+22!)/44 = 20! * 11
Hence, the simplified expression of (20!+21!+22!)/44 is 20! * 11
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