# All Questions

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### Is there a name for the closed form of $\sum_{n=0}^{\infty} \frac{1}{1+ a^n}$?

I hope this is not a duplicate question. If we modify the well known geometric series, with $a>1$, to $$\sum_{n=0}^{\infty} \frac{1}{1+a^n}$$ is there a closed form with a name? I suspect ...
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### Maximal $n$ such the the additive partition with a given product is unique.

Given $n$, there are many tuples with $a + b + c = n,a < b < c$. For large $n$, different tuples may give the same products. E.g. $2+8+9=19=3+4+12,2\times8\times9=144=3\times4\times12$. What is ...
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### How to solve a bi-quadratic equation with symbolic coefficients?

I have the following equation with the symbolic coefficients specified using 'syms' which i have been trying to solve in MATLAB:- ...
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### How to estimate magnitude of expontent?

When given an exponent, such as 6^12, is there a simple way to approximate how large(magnitude) the result is, without performing the calculation? Is this method accurate for large exponents?
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### cross-sections of a sphere bundle

Let $B$ be a CW-complex (or a manifold) and $B_0$ a CW-subcomplex (or a submanifold) of $B$. Let $\xi=(E,p,B)$ be a fibre bundle with fibre $S^n$. Choose a basepoint $*\in S^n$. Let $\Gamma(\xi)$ be ...
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### Map to $RP^2 \vee S^1$ nullhomotopic

Let $R$ be $S^{1}\vee S^{1}$. Call the first circle by $a$ and second one by $b$. Let $X$ be space by attaching two $2$-cells to $R$ one via the boundry map $a^{3}$ and the other via the boundry ma ...
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### $2$-adic sequence converging to $\sqrt{-7}$.

I am trying to construct a sequence in $\mathbb Q_2$ that is formed of rational numbers and converges to $\sqrt{-7}$, to prove that $(\mathbb Q, |\cdot|_2)$ is not complete. My lecturer stated that ...
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### Determine clockwise or anticlockwise

I have a central point define by an x and y and I have an object which is moving around it with a location defined by an x and a y. I'm trying to determine if the object is moving clockwise or ...
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### Non-finitely generated, non-divisible, non-projective, flat module, over a polynomial ring

(1) Let $R=k[x_1,\ldots,x_n]$. I wish to find an example of a non-finitely generated, non-divisible, non-projective, flat $R$-module. Notice that $k(x_1,\ldots,x_n)$ is NOT an example of what I am ...
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### Will numerical routines for the Exponential Integral function E_n work when n is continuous?

So I am a mathematical biologist of sorts. I rely heavily on Mathematica which often provides analytic results couched in terms of special functions which I then try to go and learn about. Right now ...
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### Solving Equations system question

We get this equation and need to solve Solve in $\mathbb{Z}$ the given equation $y(y -x )(x+1) = 12\$
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### If $gcd(a,b)=1$, then there exists integers x and y such that $xa + yb = 1$

Did not find this from this website... If $$gcd(a,b)=1,$$ then there exists integers x and y such that $$xa+yb=1.$$ Now, the tip is to use particular corollary, that states: The class $[m]_{n}$ ...
Find the points at which the polar curve $r=2+2\sin{(\theta)}$ has a horizontal or vertical tangent line. Translate the parametric equation to Cartesian coordinates:  r^2=2r+2r\sin{(\theta)} ...