I'm currently working on a problem, and I think that the key to solving it requires me to find a closed-form expression for $$\sum_{i = 0}^{(n - 1)! - 1} C(n!, i)$$ Does a closed-form expression for the above even exist? Not sure if I'm totally on the wrong track. Any help would be really appreciated.
2026-03-30 08:31:26.1774859486
Need help finding a closed form for sum of combinations
68 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in SUMMATION
- Computing:$\sum_{n=0}^\infty\frac{3^n}{n!(n+3)}$
- Prove that $1+{1\over 1+{1\over 1+{1\over 1+{1\over 1+...}}}}=\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+...}}}}$
- Fourier series. Find the sum $\sum_{n=1}^\infty \frac{(-1)^{n+1}}{2n+1}$
- Sigma (sum) Problem
- How to prove the inequality $\frac{1}{n}+\frac{1}{n+1}+\cdots+\frac{1}{2n-1}\geq \log (2)$?
- Double-exponential sum (maybe it telescopes?)
- Simplify $\prod_{k=1}^{l} \sum_{r=d}^m {{m}\choose{r}} \left(N-k \right)^{r} k^{m-r+1}$
- Sum of two martingales
- How can we prove that $e^{-jωn}$ converges at $0$ while n -> infinity?
- Interesting inequalities
Related Questions in COMBINATIONS
- Selection of "e" from "e"
- Selection of at least one vowel and one consonant
- Probability of a candidate being selected for a job.
- Proving that no two teams in a tournament win same number of games
- Selecting balls from infinite sample with certain conditions
- Divide objects in groups so that total sum of sizes in a group are balanced across groups
- Value of n from combinatorial equation
- Number of binary sequences with no consecutive ones.
- Count probability of getting rectangle
- Sum of all numbers formed by digits 1,2,3,4 & 5.
Related Questions in CLOSED-FORM
- How can I sum the series $e^{-2}\frac{(3)^n}{n!}\sum_{k=0}^{\infty}\left ( \frac{1}{2}\right )^k\frac{1}{(k-n)!}$
- Computing $\int_0^\pi \frac{dx}{1+a^2\cos^2(x)}$
- Can one solve $ \int_{0}^\infty\frac{\sin(xb)}{x^2+a^2}dx $ using contour integration?
- Finding a closed form for a simple product
- For what value(s) of $a$ does the inequality $\prod_{i=0}^{a}(n-i) \geq a^{a+1}$ hold?
- Convergence of $\ln\frac{x}{\ln\frac{x}{\ln x...}}$
- How can one show that $\int_{0}^{1}{x\ln{x}\ln(1-x^2)\over \sqrt{1-x^2}}\mathrm dx=4-{\pi^2\over 4}-\ln{4}?$
- Exercises about closed form formula of recursive sequence.
- Simplify and determine a closed form for a nested summation
- Direction in closed form of recurrence relation
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Not in terms of elementary functions. https://www.wolframalpha.com/input/?i=sum+from+i%3D%28n-1%29%21+to+n%21+of+C%28n%21%2C+i%29