How to find the smallest n for inequality involving factorial, $n! > 10^6 $, what is n?
I solved it using calculator, that is the answer is $n \approx 9$. How to solve this inequality?
Smallest $n$ giving $n! > 10^6$ ?
Edit inequality relation
2026-03-31 23:29:22.1774999762
How to find the smallest n for inequality involving factorial, $n! > 10^6 $, what is $n$?
136 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in CONTEST-MATH
- Solution to a hard inequality
- Length of Shadow from a lamp?
- All possible values of coordinate k such that triangle ABC is a right triangle?
- Prove that $1+{1\over 1+{1\over 1+{1\over 1+{1\over 1+...}}}}=\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+...}}}}$
- Lack of clarity over modular arithmetic notation
- if $n\nmid 2^n+1, n|2^{2^n+1}+1$ show that the $3^k\cdot p$ is good postive integers numbers
- How to prove infinitely many integer triples $x,y,z$ such that $x^2 + y^2 + z^2$ is divisible by $(x + y +z)$
- Proving that $b-a\ge \pi $
- Volume of sphere split into eight sections?
- Largest Cube that fits the space between two Spheres?
Related Questions in QUADRATICS
- Do you have to complete the square before using the quadratic formula?
- Roots of the quadratic eqn
- Questions on positivity of quadratic form with orthogonal constraints
- Conjugate quadratic equations
- Do Irrational Conjugates always come in pairs?
- Quadratic Equations and their roots.
- Solving a quadratic equation with square root constants.
- What would the roots be for this quadratic equation $f(x)=2x^2-6x-8$?
- Polynomial Equation Problem with Complex Roots
- Solve $\sin^{-1}x+\sin^{-1}(1-x)=\cos^{-1}x$ and avoid extra solutions while squaring
Related Questions in FACTORIAL
- How is $\frac{\left(2\left(n+1\right)\right)!}{\left(n+1\right)!}\cdot \frac{n!}{\left(2n\right)!}$ simplified like that?
- Remainder of $22!$ upon division with $23$?
- What is the name of this expression?
- How to compute $\left(\frac{n-1}{2}\right)!\pmod{n}$ fast?
- Proving $\sum_{k=1}^n kk!=(n+1)!−1$
- How do we know the Gamma function Γ(n) is ((n-1)!)?
- Approximate value of $15!$
- Limit of a Sequence involving factorials
- How to understand intuitively the fact that $\log(n!) = n\log(n) - n + O(\log(n))$?
- Deriving the fact that the approximation $\log(n!) \approx n\log(n) - n + \frac{1}{2}\log(2\pi n)$ is $O(1/n)$.
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?
$$ \begin{align*} 9!&=1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9\\ &=(2\cdot5)(3\cdot7)(4\cdot6)(8\cdot9)\\ &<10\cdot 30\cdot 30\cdot 80\\ &<8\cdot10^5\\ &<10^6. \end{align*} $$ and $$ \begin{align*} 10!&=1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9\cdot10\\ &=(2\cdot5)(3\cdot7)(4\cdot6)(8\cdot9)\cdot10\\ &>10\cdot 20\cdot 20\cdot 70\cdot 10\\ &=28\cdot10^5\\ &>2\cdot10^6\\ &>10^6. \end{align*} $$