$$ \sum_{p \, \in \text{ primes}} \frac{1}{2^p} $$
My friend came across a book which claimed this to be irrational and claimed it could be solved using the pigeonhole principle.
2026-03-26 01:10:26.1774487426
Is $\sum_{p} \frac{1}{2^p}$ irrational?
79 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in SEQUENCES-AND-SERIES
- How to show that $k < m_1+2$?
- Justify an approximation of $\sum_{n=1}^\infty G_n/\binom{\frac{n}{2}+\frac{1}{2}}{\frac{n}{2}}$, where $G_n$ denotes the Gregory coefficients
- Negative Countdown
- Calculating the radius of convergence for $\sum _{n=1}^{\infty}\frac{\left(\sqrt{ n^2+n}-\sqrt{n^2+1}\right)^n}{n^2}z^n$
- Show that the sequence is bounded below 3
- A particular exercise on convergence of recursive sequence
- Proving whether function-series $f_n(x) = \frac{(-1)^nx}n$
- Powers of a simple matrix and Catalan numbers
- Convergence of a rational sequence to a irrational limit
- studying the convergence of a series:
Related Questions in PRIME-NUMBERS
- New prime number
- Confirmation of Proof: $\forall n \in \mathbb{N}, \ \pi (n) \geqslant \frac{\log n}{2\log 2}$
- How do I prove this question involving primes?
- What exactly is the definition of Carmichael numbers?
- I'm having a problem interpreting and starting this problem with primes.
- Decimal expansion of $\frac{1}{p}$: what is its period?
- Multiplying prime numbers
- Find the number of relatively prime numbers from $10$ to $100$
- A congruence with the Euler's totient function and sum of divisors function
- Squares of two coprime numbers
Related Questions in PIGEONHOLE-PRINCIPLE
- Is it possible to make a computer network of 75 computers
- Pigeonhole principle: prove that a class of 21 has at least 11 male or 11 female students.
- Proving that a set of 2016 natural numbers contain a non-empty set with a sum divisible by 2016
- Question on proof of Erdos and Szekeres
- Pigeon Hole Principle Proof integrated with sets
- # of vertices and # of connected components proof problem?
- Prove that any collection of 8 distinct integers contains distinct x and y such that x - y is divisible by 7.
- Hint for problem on $4 \times 7$-chessboard problem related to pigeonhole principle
- Pigeonhole principle subsets
- $80$ balls in a row. $50$ of them are yellow and $30$ are blue. Prove that there are at least $2$ blue balls with a distance of exactly $3$ or $6$.
Related Questions in RATIONALITY-TESTING
- Irrationality of $\log_2(2015)$
- Find an equation where all 'y' is always irrational for all integer values of x
- What is Euler doing?
- Is there an essential difference between Cartwright's and Niven's proofs of the irrationality of $\pi$?
- $\sqrt{\frac{\pi e}{2}}=\frac{1}{1+\mathrm{K}_{i=1}^{\infty}{\frac{i}{1}}}+\sum_{n=0}^{\infty}{\frac{1}{(2n+1)!!}}$ implies $\sqrt{\pi e/2}\notin Q$?
- Rationality of circumference of an ellipsis with rational semi-axes
- Rationality of the Gamma function
- Can we find smallest positive $x$ such that $\pi^x$ is rational?
- For the expression $\sqrt{\frac{x}{y}}$ to be rational, is it necessary for both to be squares?
- Spivak Calculus 4-th Ed., Chapter 2, Exercise 13a, Understanding the proof of $\sqrt3$ being irrational.
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?