Question

Solve for x :-

1/20! + 1/21! = x/22!

Answer 1

Answer:

= 1/20! + 1/21! = x/22!

= 1/2 4 3 2 9 0 2 0 0 8 1 7 6 6 4 0 0 0 0 + 1/51090942171709440000 = x/22!

= 1/2322315553259520000 = x/22!

= 1/2322315553259520000 = x/1124000727777607680000

= x/1124000727777607680000 = 1/2322315553259520000

= x = 1/2322315553259520000 x 1124000727777607680000

= x = 484

Answer 2

Question :- Solve for x :-

$\rm \: \dfrac{1}{20!} + \dfrac{1}{21!} = \dfrac{x}{22!}$

$\large\underline{\sf{Solution-}}$

Given expression is

$\rm \: \dfrac{1}{20!} + \dfrac{1}{21!} = \dfrac{x}{22!}$

can be rewritten as on multiply by 22!,

$\rm \: \dfrac{22!}{20!} + \dfrac{22!}{21!} = x$

can be further rewritten as

$\rm \: \dfrac{22.21. \: 20!}{20!} + \dfrac{22. \: 21!}{21!} = x$

$\rm \: x = 22 \times 21 + 22$

$\rm \: x = 22(21 + 1)$

$\rm \: x = 22 \times 22$

$\rm\implies \:\rm \: x = 484$

$\rule{190pt}{2pt}$

Short Cut Trick :-

$\boxed{\rm{  \:\rm \: If \: \dfrac{1}{(n - 2)!} + \dfrac{1}{(n - 1)!} = \dfrac{x}{n!} \: \: then \: x \: = \: {n}^{2} \: }}$

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: to \: know}}}} \\ \\ \bigstar \: \bf{0! = 1}\\ \\ \bigstar \: \bf{1! = 1 }\\ \\ \bigstar \: \bf{ 2! = 2}\\ \\ \bigstar \: \bf{3! = 6 }\\ \\\bigstar \: \bf{4! = 24}\\ \\ \bigstar \: \bf{5! = 120}\\ \\ \bigstar \: \bf{6! = 720}\\ \\ \bigstar \: \bf{7! = 5040}\\ \\ \bigstar \: \bf{8! = 40320}\\ \\ \end{array} }}\end{gathered}\end{gathered}\end{gathered}$