Simplifying Factorials: Proving (n+1)(n+1)!+(n+1)! =(n+2)!

AI Thread Summary
The discussion focuses on simplifying the equation (n+1)(n+1)! + (n+1)! to prove that it equals (n+2)!. Participants suggest starting by factoring the left-hand side, which leads to the expression [(n+1)!][(n+1)+1]. The simplification process is emphasized as a key step to demonstrate the equality. The original poster expresses confusion and a lack of confidence in their ability to tackle the problem. Overall, the conversation centers on understanding factorial simplification in discrete mathematics.
hammonjj
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Homework Statement


(n+1)(n+1)!+(n+1)! =(n+2)! simplify

The Attempt at a Solution


I need to know how to simplify this to show it is true. I know that the above statement is true, but I do not understand how to simplify the left hand side to show it.

Thanks, I really have no idea where to begin and, frankly, it's kind of embarrassing as this is for a discrete math class :(

Thanks!
 
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Factorize LHS then you will get [(n+1)!][(n+1)+1] :smile:
 
hammonjj said:

Homework Statement


(n+1)(n+1)!+(n+1)! =(n+2)! simplify

The Attempt at a Solution


I need to know how to simplify this to show it is true. I know that the above statement is true, but I do not understand how to simplify the left hand side to show it.

Thanks, I really have no idea where to begin and, frankly, it's kind of embarrassing as this is for a discrete math class :(

Thanks!
What is (n+1)x + x ?
 

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