If \(\frac{1}{4!} +\frac{1}{5!} = \frac{x}{6!}\), find the value of x

1.	If \(\frac{1}{4!} +\frac{1}{5!} = \frac{x}{6!}\), find the value of x.
Answer» To Find: Value of n Given: \(\frac{1}{4!} +\frac{1}{5!} = \frac{x}{6!}\) Formula Used: n! = (n) × (n-1) × (n-2) × (n-3) ………. 3 × 2 × 1 Now, \(\frac{1}{4!} +\frac{1}{5!} = \frac{x}{6!}\) ⇒ \(\frac{1}{24} +\frac{1}{120} = \frac{x}{720}\) (4! = 24, 5! = 120) ⇒ \(\frac{5+1}{120}=\frac{x}{720}\) ⇒ \(\frac{6}{120}=\frac{x}{720}\) ⇒ x = 36

If \(\frac{1}{4!} +\frac{1}{5!} = \frac{x}{6!}\), find the value of x.

Answer»

To Find: Value of n

Given: \(\frac{1}{4!} +\frac{1}{5!} = \frac{x}{6!}\)

Formula Used: n! = (n) × (n-1) × (n-2) × (n-3) ………. 3 × 2 × 1

Now, \(\frac{1}{4!} +\frac{1}{5!} = \frac{x}{6!}\)

⇒ \(\frac{1}{24} +\frac{1}{120} = \frac{x}{720}\) (4! = 24, 5! = 120)

⇒ \(\frac{5+1}{120}=\frac{x}{720}\)

⇒ \(\frac{6}{120}=\frac{x}{720}\)

⇒ x = 36