is this a geometric series?

[corsec]

x + x^2 + x^3 + x^4 + x^5 + x^6
----- ----- ----- ----- ------
2 4 8 16 32

I've tried putting together several substitutes
if I put 2 as x I get a ratio of which would be x
if I try 3 I get a lot different results
if I try 4 I get an even different answer
so I can't get a ratio that seems to work for it

 

[tkhunny]

Divide successive terms and see if you get a common ratio.

 

[corsec]

diving successive terms I believe the ratio is going to be

x
---
2x

does this sound right?

 

[galactus]

\(\displaystyle \L\\\sum_{n=0}^{5}\frac{x^{n+1}}{2^{n}}=x+\frac{x^{2}}{2}+\frac{x^{3}}{4}+\frac{x^{4}}{8}+\frac{x^{5}}{16}+\frac{x^{6}}{32}\)

 

[stapel]

x + x^2 + x^3 + x^4 + x^5 + x^6
----- ----- ----- ----- ------
2 4 8 16 32

Is the above meant to be as follows?

. . . . .\(\displaystyle \large{\frac{x}{2}\,+ \,\frac{x^2}{4}\,+ \,\frac{x^3}{8}\,+ \,\frac{x^4}{16}\,+ \,\frac{x^5}{32}\,+ x^6}\)


It appears to me that a denominator may be missing...?

diving successive terms I believe the ratio is going to be
x
---
2x

Is the above "x/(2x)"? That is, "1/2" after simplifying?

Thank you.

Eliz.

 

[corsec]

thank you for your help so far. I divided subsequent terms and the ratio I got was x/2 maybe that's wrong. I'm still not sure what the exact ratio would be and if the series would be arithmetic, geometric or neither (if there is no consistant ratio or difference between the terms)

 

[pka]

The first term is x.
The common ratio is x/2.
Multiply any term by x/2 to get the next term.