Show that the sum $$ S = \frac{1}{\sqrt{2}}+ \frac{1}{\sqrt{3}} + \dots + \frac{1}{\sqrt{n}} $$ cannot be an integer for any value of $n$. I am completely stumped any help would be welcome.
2026-04-09 07:52:11.1775721131
sum of reciprocals of square roots cannot be an integer
66 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 IRRATIONAL-NUMBERS
- Convergence of a rational sequence to a irrational limit
- $\alpha$ is an irrational number. Is $\liminf_{n\rightarrow\infty}n\{ n\alpha\}$ always positive?
- Is this : $\sqrt{3+\sqrt{2+\sqrt{3+\sqrt{2+\sqrt{\cdots}}}}}$ irrational number?
- ls $\sqrt{2}+\sqrt{3}$ the only sum of two irrational which close to $\pi$?
- Find an equation where all 'y' is always irrational for all integer values of x
- Is a irrational number still irrational when we apply some mapping to its decimal representation?
- Density of a real subset $A$ such that $\forall (a,b) \in A^2, \ \sqrt{ab} \in A$
- Proof of irrationality
- Is there an essential difference between Cartwright's and Niven's proofs of the irrationality of $\pi$?
- Where am I making a mistake in showing that countability isn't a thing?
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?