# Linked Questions

79 questions linked to/from Value of $\sum\limits_n x^n$
7answers
856 views

### Proof of the formula $1+x+x^2+x^3+ \cdots +x^n =\frac{x^{n+1}-1}{x-1}$ [duplicate]

Possible Duplicate: Value of $\sum x^n$ Proof to the formula $$1+x+x^2+x^3+\cdots+x^n = \frac{x^{n+1}-1}{x-1}.$$
5answers
300 views

### Easy summation question: $S= 1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\frac{1}{16}\cdots$ [duplicate]

While during physics I encountered a sum I couldn't evaluate: $$S= 1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\frac{1}{16}\cdots$$ Is there a particular formula for this sum and does it converges?
1answer
9k views

### How to convert a series to an equation? [duplicate]

Possible Duplicate: Value of $\sum\limits_n x^n$ I don't know the technical language for what I'm asking, so the title might be a little misleading, but hopefully I can convey my purpose to you ...
4answers
444 views

2answers
357 views

### Formulas for series that are not geometric [duplicate]

Possible Duplicate: Value of $\sum\limits_n x^n$ Ive been studying Geometric series and Arithmetic series all day and have struggled to attempt these problems. The Question is to sum up these ...
5answers
75 views

### Why is $5 + 5z + 5z^2 + … + 5z^{11} = \frac{(5z^{12} - 5)}{(z - 1)}$? [duplicate]

Why is $5 + 5z + 5z^2 + ... + 5z^{11} = \frac{(5z^{12} - 5)}{(z - 1)}$ ? I don't understand how you can rewrite it to that. Z is in this case a complex number: (for example: \$z = 0,8(0,5 + 0,5i\...

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