Factorials - Prove 1/9! + 1/10! + 1/11! = 122/11!

Question:

Prove 1/9! + 1/10! + 1/11! = 122/11!


Solution:

LHS

1/9! + 1/10! + 1/11!

= (11 x 10) / (11 x 10 x 9!) + 11 / (11 x 10!) + 1 / 11!

= (11 x 10) / (11 x 10!) + 11 / (11 x 10!) + 1 / 11!

= (11 x 10) / 11! + 11 / 11! + 1 / 11!

= 110 + 11 + 1 / 11!

= 122 / 11!

= RHS


Answer:

1/9! + 1/10! + 1/11! = 122/11! since LHS = RHS


Solution Video:



Prove 1/9! + 1/10! + 1/11! = 122/11! A solved example on Factorials in Permutations and Combinations