query: For integer $n>1$, can $\sum_{k=1}^{n}\sqrt{k}$ be a rational number? Can it be an integer?
positive_passages.docid: 104917
positive_passages.text: Is $\sqrt1+\sqrt2+\dots+\sqrt n$ ever an integer?
negative_passages.docid: 103840
negative_passages.text: Calculate $\sum_{k=1}^n k2^{n-k}$
negative_passages.docid: 47357
negative_passages.text: Does the series $\sum_{n=1}^{\infty}|x|^\sqrt n$ converge pointwise? If it then what would be the sum?
negative_passages.docid: 35837
negative_passages.text: How to prove that any (integer)$^{1/n}$ that isn't an integer, is irrational?
negative_passages.docid: 42810
negative_passages.text: Is $(\mathbb{Q},+)$ isomorphic to $(\mathbb{Q}^n,+)$?
negative_passages.docid: 1383
negative_passages.text: How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
negative_passages.docid: 101052
negative_passages.text: Find the infinite sum $\sum_{k=1}^{\infty}\sqrt k - 2\sqrt {k + 1} + \sqrt {k + 2} $
negative_passages.docid: 144568
negative_passages.text: How closely can we estimate $\sum_{i=0}^n \sqrt{i}$
negative_passages.docid: 82636
negative_passages.text: Maybe is right $\frac{n^2 + 1}{4k + 3} \notin \mathbb{Z}, n, k \in \mathbb{N}^{+}$
negative_passages.docid: 19676
negative_passages.text: Is it known whether ${\sqrt{2}}^{\sqrt{2}}$ is irrational?
negative_passages.docid: 134311
negative_passages.text: How to determine equation for $\sum_{k=1}^n k^3$
negative_passages.docid: 104753
negative_passages.text: $\sum_{k=1}^nH_k = (n+1)H_n-n$. Why?
negative_passages.docid: 46606
negative_passages.text: Can an integer of the form $4n+3$ written as a sum of two squares?
negative_passages.docid: 56802
negative_passages.text: Why $\sqrt[3]{{2 + \sqrt 5 }} + \sqrt[3]{{2 - \sqrt 5 }}$ is a rational number?
negative_passages.docid: 134765
negative_passages.text: Is an integer a sum of two rational squares iff it is a sum of two integer squares?
negative_passages.docid: 2932
negative_passages.text: How do I prove this sum is not an integer
negative_passages.docid: 73255
negative_passages.text: $ S_n=\sum_{k=1}^n\frac{1}{k}$ then is $S_n$ bounded?