Is there a known formula to the sum $$1+\sqrt{2}+\sqrt{3}+\cdots+\sqrt{N}$$ where $N$ is some natural number? Thanks
2026-04-18 10:29:11.1776508151
Is there a formula for $1+\sqrt{2}+\sqrt{3}+\cdots+\sqrt{N}$?
90 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in CALCULUS
- Equality of Mixed Partial Derivatives - Simple proof is Confusing
- How can I prove that $\int_0^{\frac{\pi}{2}}\frac{\ln(1+\cos(\alpha)\cos(x))}{\cos(x)}dx=\frac{1}{2}\left(\frac{\pi^2}{4}-\alpha^2\right)$?
- Proving the differentiability of the following function of two variables
- If $f ◦f$ is differentiable, then $f ◦f ◦f$ is differentiable
- Calculating the radius of convergence for $\sum _{n=1}^{\infty}\frac{\left(\sqrt{ n^2+n}-\sqrt{n^2+1}\right)^n}{n^2}z^n$
- Number of roots of the e
- What are the functions satisfying $f\left(2\sum_{i=0}^{\infty}\frac{a_i}{3^i}\right)=\sum_{i=0}^{\infty}\frac{a_i}{2^i}$
- Why the derivative of $T(\gamma(s))$ is $T$ if this composition is not a linear transformation?
- How to prove $\frac 10 \notin \mathbb R $
- Proving that: $||x|^{s/2}-|y|^{s/2}|\le 2|x-y|^{s/2}$
Related Questions in NUMBER-THEORY
- Maximum number of guaranteed coins to get in a "30 coins in 3 boxes" puzzle
- Interesting number theoretical game
- Show that $(x,y,z)$ is a primitive Pythagorean triple then either $x$ or $y$ is divisible by $3$.
- About polynomial value being perfect power.
- Name of Theorem for Coloring of $\{1, \dots, n\}$
- Reciprocal-totient function, in term of the totient function?
- What is the smallest integer $N>2$, such that $x^5+y^5 = N$ has a rational solution?
- Integer from base 10 to base 2
- How do I show that any natural number of this expression is a natural linear combination?
- Counting the number of solutions of the congruence $x^k\equiv h$ (mod q)
Related Questions in ELEMENTARY-NUMBER-THEORY
- Maximum number of guaranteed coins to get in a "30 coins in 3 boxes" puzzle
- Interesting number theoretical game
- How do I show that if $\boldsymbol{a_1 a_2 a_3\cdots a_n \mid k}$ then each variable divides $\boldsymbol k $?
- Using only the digits 2,3,9, how many six-digit numbers can be formed which are divisible by 6?
- Algebra Proof including relative primes.
- How do I show that any natural number of this expression is a natural linear combination?
- Counting the number of solutions of the congruence $x^k\equiv h$ (mod q)
- algebraic integers of $x^4 -10x^2 +1$
- What exactly is the definition of Carmichael numbers?
- Number of divisors 888,888.
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 RECREATIONAL-MATHEMATICS
- Good ideas for communicating the joy of mathematics to nine and ten year olds
- Who has built the house of Mason?
- Is there any tri-angle ?
- In what position , the dogs will reside?
- existence of solutions of $a^n+b^n+c^n=6^n$
- Sushi Go! and optimal passing strategy
- Cut the letter $M$ to obtain $9$ single triangles by drawing $3$ straight lines
- Tennis balls problem from John H Conway's "Genius At Play"
- The Heegner Polynomials
- 2018 January Challenge: Prove inequality in geometry problem
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?