Linked Questions

4
votes
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 $$1+x+x^2+x^3+\cdots+x^n = \frac{x^{n+1}-1}{x-1}.$$
2
votes
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?
2
votes
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 ...
1
vote
4answers
444 views

Power summation of $n^3$ or higher [duplicate]

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+...
-1
votes
3answers
2k views

Why $ \sum_{k=0}^{\infty} q^k $ sum is $ \frac{1}{1-q}$ when $|q| < 1$ [duplicate]

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 ...
-3
votes
4answers
15k views

Proof of the power series 1 + $x^2$ + $x^3$ + $\ldots$ + $x^n$ = $\frac{1}{1-x}$ [duplicate]

Can anyone show me the proof of why if $|x|<1$ then: $$ \lim_{n \to \infty} 1+ x^2 + x^3 + \ldots + x^n = \frac{1}{1-x} $$
5
votes
5answers
326 views

Evaluating the sum of geometric series [duplicate]

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 ...
-1
votes
2answers
2k views

Simplifying the infinite series $\sum_{n = 1}^{\infty} \left(\frac{1}{2}\right)^{3n}$ [duplicate]

Does anyone know of a way to simplify $$ \sum_{n = 1}^{\infty} \left(\frac{1}{2}\right)^{3n} $$ to a number?
0
votes
3answers
236 views

Prove that 1/2 + 1/4 + 1/8 … = 1 [duplicate]

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 ...
3
votes
2answers
143 views

$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\cdots+\frac{1}{\infty}=?$ [duplicate]

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 ...
-1
votes
4answers
140 views

How to calculate $k^0+k^1+k^2 + k^3+…+ k^{n-1}$ [duplicate]

How to simplify below expression or convert it to something simpler like $k^{n-1}$? $$ k^0+k^1+k^2 + k^3+...+ k^{n-1} $$
-4
votes
7answers
215 views

Find the sum of the geometric sequence [duplicate]

$$1+ \frac12 + \frac14+\dots+\frac1{2^n}$$ 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 $...
1
vote
4answers
127 views

What is the formula of: $a^{0} + a^{1} + a^{2} + … + a^{n-1} + a^{n}$? [duplicate]

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