Geometric series

Jan 2010
142
0
is the right equation for S_n= 1+x+x^2+x^3+...+x^(n-1) ?

\(\displaystyle \sum_x^{\infty} \frac{1-x^(n-1)}{1-x} \)

the numerator is 1-x^(n-1)


is the right equation?

thanks!
 
Aug 2008
74
23
you should edit your post cause it's completely confusing.

if you're asking about what is the sum of 1+x+x^2+...+x^(n-1) equal to, then the answer is (1-x^n)/(1-x)
 
Jan 2010
142
0
you should edit your post cause it's completely confusing.

if you're asking about what is the sum of 1+x+x^2+...+x^(n-1) equal to, then the answer is (1-x^n)/(1-x)

I tried to fix it but the exponent of n-1 always messed up.

Thanks for the help, I wasnt sure if i did it right...

Can you give me example using this (1-x^n/1-x) thanks...
 

Prove It

MHF Helper
Aug 2008
12,883
4,999
I tried to fix it but the exponent of n-1 always messed up.

Thanks for the help, I wasnt sure if i did it right...

Can you give me example using this (1-x^n/1-x) thanks...
Write your exponents inside {}.

So you need to write 1 - x^{n - 1} to get \(\displaystyle 1 - x^{n - 1}\).
 
Jan 2010
142
0
Write your exponents inside {}.

So you need to write 1 - x^{n - 1} to get \(\displaystyle 1 - x^{n - 1}\).

\(\displaystyle S_n= 1+x+x^2+x^3+...+x^{n-1} ? \)
=
\(\displaystyle \sum_{x=\infty}^{n-1} a_1 \frac{1-x^n}{1-x} \)

right?

im looking for \(\displaystyle S_7 \) using the the formula. I don't know how to start because I don't have variables for x.