Factorials :/ (1 Viewer)

[yellowhighlighterr]

I got part a, but its application into part b confuses me. The answer is meant to be:



could i have some help pls? thanks

 

[cossine]

View attachment 39032

I got part a, but its application into part b confuses me. The answer is meant to be:

View attachment 39033

could i have some help pls? thanks

telescoping sum.

 

[yellowhighlighterr]

telescoping sum.

This is year 12? This is a year 11 question-

 

[Vall]

can’t we just sub the identity from (i) into (ii)?
so the thing in part two becomes:
= (2! - 1!) + (3! - 2!) + (4!! - 3!) + … + ((n - 1)! - n!) + (n! - (n-1)!) + ((n+1)! - n!)
= (n+1)! - 1
(all the terms cancel out except those two)