Intereting Posts

If $F$ is a formally real field then is $F(\alpha)$ formally real?
Can the intersection of open or closed balls be empty, if their radii are bounded from below?
Is $ \pi $ definable in $(\Bbb R,0,1,+,×, <,\exp) $?
Diagonalization and eigenvalues
A cone inscribed in a sphere
Show that $\int_0^1\ln(-\ln{x})\cdot{\mathrm dx\over 1+x^2}=-\sum\limits_{n=0}^\infty{1\over 2n+1}\cdot{2\pi\over e^{\pi(2n+1)}+1}$ and evaluate it
How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$
Gauss Elimination with constraints
PDE Evans, 1st edition, Chapter 5, Problem 14
An inequality in the proof of characterization of the $H^{-1}$ norm in Evans's PDE book
How to show if $\sqrt{n} $ is rational number then $n$ is a perfect square?
Cardinality of quotient ring $\mathbb{Z_6}/(2x+4)$
Prove that a connected space cannot have more than one dispersion points.
Is $\int_0^\infty\frac{|\cos(x)|}{x+1} dx$ divergent?
Graph with girth 5 and exactly $k^2+1$ vertices

Suppose the expression is given like this:

$(1+x) ^{10} (1+x)^{20}$. How can I find out the coefficient of $x^m$ in the above expression, given that $0≤m≤20$.

- sum of binomial coefficients involving $n,p,q,r$
- If $p$ and $q$ are primes, which binomial coefficients $\binom{pq}{n}$ are divisible by $pq$?
- Sum of square binomial coefficients
- Spivak's Calculus - Exercise 4.a of 2nd chapter
- Finding divisibility of a
- Stirling's Approximation for binomial coefficient
- How to prove combinatorial identity $\sum_{k=0}^s{s\choose k}{m\choose k}{k\choose m-s}={2s\choose s}{s\choose m-s}$?
- Evaluate a finite sum with four factorials
- Show that $\sum_{k=0}^n\binom{3n}{3k}=\frac{8^n+2(-1)^n}{3}$
- How to show $\sum_{i=1}^{n} \binom{i}{2}=\binom{n+1}{3}$?

Using binomial expansion, the problem can be solved. For example, if *m* = 7, you know that 7 can be written as 7+0, 6+1, 5+2, 4+3, 3+4, 2+5, 1+6 or 0+7.

Now, using the result above, break down the expression into two separate expressions, and find the coefficient for each of the required powers of *x* using the formula for *n*th term of a binomial expansion.

- Request for Statistics textbook
- Looking for a proof of Cleo's result for ${\large\int}_0^\infty\operatorname{Ei}^4(-x)\,dx$
- Proof: Tangent space of the general linear group is the set of all squared matrices
- Proof that $26$ is the one and only number between square and cube
- A linear map $S:Y^*\to X^*$ is weak$^*$ continuous if and only if $S=T^*$ for som $T\in B(X,Y)$
- Integral domain that is integrally closed, one-dimensional and not noetherian
- How prove this $|ON|\le \sqrt{a^2+b^2}$
- $f(\alpha x) = f(x)^{\beta}$ under different constraints
- Real Analysis : uniform convergence of sequence
- For matrices $A$ and $B$, $B-A\succeq 0$ (i.e. psd) implies $\text{Tr}(B)\geq \text{Tr}(A)$ and $\det(B)\geq\det(A)$
- Proving an invertible matrix which is its own inverse has determinant $1$ or $-1$
- Let $G$ be a finite group with $|G|>2$. Prove that Aut($G$) contains at least two elements.
- How to prove that exponential grows faster than polynomial?
- Polynomial approximation of circle or ellipse
- Solving Partial Differential Equation with Self-similar Solution