Question

Quick series question....Can anyone quickly explain why (k+1)! = (k+1)k!

Answer 1

n!= n (n-1)
(k+1)!=(k+1)(k+1-1)=(k+1)(k)

...wait is there really a factorial sign after k on the right side?

Answer 2

yeah

Answer 3

From what it shows it shows one example before which is K! = k(k-1)....(2)(1)

Answer 4

and then the next is (k+1)! = (k+1)k!....

Answer 5

hmm maybe this can help you
http://www.themathpage.com/aprecalc/factorial.htm
See example 5

Answer 6

Do you think it would be a fair statement to say that (k+1)k! = (k+1)!k

Answer 7

(k+1)k! = (k+1) [(k)(k-1)(k-2).......x1] = (k+1)!
Now what do you think?

Answer 8

By Definition :- k! = k(k-1)(k-2)....(3)(2)(1)
Now substitute k+1 for k in the above definition:
(k+1)! = (k+1)(k)(k-1)(k-2)........(3)(2)(1)
Observe that after k+1 all the other terms multiply to yield k!.
Thus, (k+1)! = (k+1)k!.
I hope that answers your query!

Answer 9

But for the statement (k+1)k! = (k+1)!k, I don't think it is correct
As I've mentioned
(k+1)k! = (k+1) [(k)(k-1)(k-2).......x1] = (k+1)!
But for the right hand side, you can see that they are not the same

Answer 10

Yes, that statement is definitely wrong.

Answer 11

maybe because it wasn't heard the first time around:

(k+1)! nobody hears the shout
(k+1) k! somebody prolly heard this one...

kidding...:) @Callisto ,@Aron_West are correct....