Linked Questions

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

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?

Can anyone show me the proof of this equation: $$ \lim_{n \to \infty} 1 + x + x^2 + x^3 + \ldots + x^n = \frac{1}{1-x}, $$ where $|x|<1$. Edit: I have then additionally written $x$ on the left ...

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 ...

Why is the infinite sum of $ \sum_{k=0}^{\infty} q^k = \frac{1}{1-q}$ when $|q| < 1$ I don't understand how the $\frac{1}{1-q}$ got calculated. I am not a math expert so I am looking for an easy ...

Possible Duplicate: why is $\sum\limits_{k=1}^{n} k^m$ a polynomial with degree $m+1$ in $n$ If I want to find the formula for $$\sum_{k=1}^n k^2$$ I would do the next: $$(n+1)^2 = a(n+1)^3 + b(n+...

Possible Duplicate: Value of $\sum\limits_n x^n$ I'm trying to understand how to evaluate the following series: $$ \sum_{n=0}^\infty {\frac{18}{3^n}}. $$ I tried following this Wikipedia ...

I've often heard that instead of adding up to a little less than one, 1/2 + 1/4 + 1/8... = 1. Is there any way to prove this using equations without using Sigma, or is it just an accepted fact? I need ...

Does anyone know of a way to simplify $$ \sum_{n = 1}^{\infty} \left(\frac{1}{2}\right)^{3n} $$ to a number?

$$1+ \frac12 + \frac14+\dots+\frac1{2^n}$$ To find the sum of the equation you have to find $n$, the number of terms in the geometric sequence and I don't know how... The answer in the text book is $...

This question concerns the infinite geometric series formula. It turns out there is a nice formula for the sum of an infinite geometric series. Consider the infinite geometric series $1+r+r^2+r^3+\...

One of my friends has given me the following problem: $$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\cdots+\frac{1}{\infty} = ?$$ He said that the answer is $1$. He has given his argument as that this is ...

How to simplify below expression or convert it to something simpler like $k^{n-1}$? $$ k^0+k^1+k^2 + k^3+...+ k^{n-1} $$

I'm sorry if this is duplicated, but I can not find any answer to it.

What is the formula of: $$a^{0} + a^{1} + a^{2} + ... + a^{n-1} + a^{n}$$ Any ideas?