For $N\in\mathbb{N}$ large enough. Can I bound this $N((1+\delta)^{2N}+1)\leq N^j$ for any $j\in \mathbb{N}$, where $\delta<1/2$? I tried using Matlab for j=5, but I'd like some ideas for a proof. Thanks.
2026-05-14 16:53:48.1778777628
Can I bound this $N((1+\delta)^{2N}+1)\leq N^j$? for any $j\in \mathbb{N}$, where $\delta<1$
30 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in INEQUALITY
- Confirmation of Proof: $\forall n \in \mathbb{N}, \ \pi (n) \geqslant \frac{\log n}{2\log 2}$
- Prove or disprove the following inequality
- Proving that: $||x|^{s/2}-|y|^{s/2}|\le 2|x-y|^{s/2}$
- Show that $x\longmapsto \int_{\mathbb R^n}\frac{f(y)}{|x-y|^{n-\alpha }}dy$ is integrable.
- Solution to a hard inequality
- Is every finite descending sequence in [0,1] in convex hull of certain points?
- Bound for difference between arithmetic and geometric mean
- multiplying the integrands in an inequality of integrals with same limits
- How to prove that $\pi^{e^{\pi^e}}<e^{\pi^{e^{\pi}}}$
- Proving a small inequality
Related Questions in EXPONENTIAL-FUNCTION
- How to solve the exponential equation $e^{a+bx}+e^{c+dx}=1$?
- derive the expectation of exponential function $e^{-\left\Vert \mathbf{x} - V\mathbf{x}+\mathbf{a}\right\Vert^2}$ or its upper bound
- How do you calculate the horizontal asymptote for a declining exponential?
- Intersection points of $2^x$ and $x^2$
- Integrate exponential over shifted square root
- Unusual Logarithm Problem
- $f'(x)=af(x) \Rightarrow f(x)=e^{ax} f(0)$
- How long will it take the average person to finish a test with $X$ questions.
- The equation $e^{x^3-x} - 2 = 0$ has solutions...
- Solve for the value of k for $(1+\frac{e^k}{e^k+1})^n$
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
geometry
circles
algebraic-number-theory
functions
real-analysis
elementary-set-theory
proof-verification
proof-writing
number-theory
elementary-number-theory
puzzle
game-theory
calculus
multivariable-calculus
partial-derivative
complex-analysis
logic
set-theory
second-order-logic
homotopy-theory
winding-number
ordinary-differential-equations
numerical-methods
derivatives
integration
definite-integrals
probability
limits
sequences-and-series
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?