Geometric Sequence

[SVang]

if the equation given is Sn=(1*1!)+(2*2!)+(3*3!)+⋯+(n*n!) , would it be a geometric sequence???

[Summer Glau]

Yeah that's a geometic sequence.

Edited December 27, 2010 by fire.realm

[SVang]

how is it geometric if it doesn't have a common ratio?

what would the conjectured equation for the sum be?

Edited December 27, 2010 by SVang

[dessskris]

Yes

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio.

(Wikipedia)

So I would say NO, the above sequence is NOT geometric.

U1=1

U2=4

U3=18

U4=96

...

Un=n*n!

Are the ratios fixed? Does the sequence have a common ratio?

NO

So they are not geometric. I guess this comes from the infinite summation IA, yeah?

The value of the sum could be found using sigma if you learn that in SL

The conjecture of the sum... I don't think I can find it but I shall spend some time trying to figure it out. I don't know, though, maybe Google could help you?

Edited December 28, 2010 by Mahuta ♥

[Mahuta ♥]

What IA and level is this?

[ILM]

So I would say NO, the above sequence is NOT geometric.

U1=1

U2=4

U3=18

U4=96

...

Un=n*n!

Are the ratios fixed? Does the sequence have a common ratio?

NO

So they are not geometric. I guess this comes from the infinite summation IA, yeah?

The value of the sum could be found using sigma if you learn that in SL

The conjecture of the sum... I don't think I can find it but I shall spend some time trying to figure it out. I don't know, though, maybe Google could help you?

I will go with Marsulipami and say no, geometric sequence should has a common, constant ratio.

This a normal series that has the explicit formula of (n*n!)

Edited December 28, 2010 by inm

[SVang]

thanks for the help!!!!

after looking it over i found that the sum of the n value is one less than the factorial of the n value above and i managed to get the conjectured expression to be (n+1)! -1.

ex: n=2 S[2]=1+4=5 n=3 3!=6 (2+1)! -1=5