I want to prove that $\sqrt{\sum a_{i}^{2}} \geq \sum \left | a_{i} \right |$, is it possible ?
2026-03-28 21:34:15.1774733655
What is the relation between the square root of the sum of squares and the sum of the absolute values?
1.9k 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 ABSOLUTE-VALUE
- To find the Modulus of a complex number
- What does $|a| = |b|$ is equal to?
- Symmetric polynomial written in elementary polynomials
- If $|ax^2+bx+c|\le \frac12$ for all $|x|\le1$, then $|ax^2+bx+c|\le x^2-\frac12$ for all $|x|\ge1$
- Proving that a double integral converges
- Equation system
- If $\sqrt{9−8\cos 40^{\circ}} = a +b\sec 40^{\circ}$, then what is $|a+b|$?
- Proving that inequalities $\|a\|_{\infty} \leq \|a\|_2 \leq \sqrt{n} \|a\|_{\infty}$ are true and sharp.
- Find a number $M$, such that $|x^3-4x^2+x+1| < M$ for all $1<x<3$
- Absolute Value of a Complex Number Inequality
Related Questions in SQUARE-NUMBERS
- Squares of two coprime numbers
- Perfect Square and its multiple
- constraints to the hamiltonian path: can one tell if a path is hamiltonian by looking at it?
- Is square root of $y^2$ for every $y>0,y\in\mathbb{R}$?
- A square root should never be negative by convention or can be proved?
- Does $x+\sqrt{x}$ ever round to a perfect square, given $x\in \mathbb{N}$?
- Proof verification: Let $gcd(x,y)=1$. If $xy$ is a perfect square, then $x$ and $y$ are perfect squares.
- How to reduce calculation time for iterative functions that involve squaring a number in every iteration. Working with numbers in millions of digits
- Digits in a perfect square problem
- Trouble with a proof. I cannot prove this without inf many proofs for each and every case.
Related Questions in SUMS-OF-SQUARES
- How many variations of new primitive Pythagorean triples are there when the hypotenuse is multiplied by a prime?
- If $x^2-dy^2 = -1$ has a solution in $\mathbb{Z^2}$, then $d$ is the sum of two coprime squares.
- How to interpret this visual proof for Archimedes' derivation of Sum of Squares?
- consecutive integers that are not the sum of 2 squares.
- Sum of the Squares of the First n square Numbers is not a perfect square number
- How many sub-square matrices does a square matrix have and is there a simple formula for it?
- On near-Pythagorean triples $(n^5-2n^3+2n)^2 + (2n^4-2n^2+1)^2 = n^{10} + 1$
- Closed form for the sum $\sum_{n=-\infty}^{\infty}\sum_{m=-\infty}^{\infty}{\left(n^2+m^2\right)^{-{p}}}$
- Prove that any power of $10$ can be written as sum of two squares
- Can Gauss-Newton algorithm give better optimization performances than Newton algorithm?
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?
Notice that $(\sum |a_i|) ^2 \geq \sum a_i^2$. Now take square roots.