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Do inequalities that hold for infinite sums hold for integrals too?

Inequality involving partial sum of $\frac{|\sin{kx}|}{k}$

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288 Answers

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29	Prove that odd perfect square is congruent to $1$ modulo $8$
22	Is $\mathbb{Z}$ isomorphic to $\bigoplus_{p\in \mathbb{P}}\mathbb{Z}_p$?
19	Find all numbers $p$ such that all six numbers $p$, $p+2$, $p+6$, $p+8$, $p+12$, $p+14$ are primes
15	Why don't we define “imaginary” numbers for every “impossibility”?
14	please solve a 2013 th derivative question?

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8,788 Reputation

+10	A question about Cauchy sequences
+5	Is $\operatorname{Aut}(\mathbb{I})$ isomorphic to $\operatorname{Aut}(\mathbb{I}^2)$?
+10	Prove that odd perfect square is congruent to $1$ modulo $8$
+5	Existence of a certain functor $F:Grpd\rightarrow Grp$

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42 Questions

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40	Trying to define $\mathbb{R}^{0.5}$ topologically [duplicate]
17	A question about connected sets in $\mathbb{R}^2$
17	Do inequalities that hold for infinite sums hold for integrals too?
15	For any two sets $A,B$ , $\|A\|\leq\|B\|$ or $\|B\|\leq\|A\|$
12	Monochromatic squares in a colored plane

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131 homework × 57	101 elementary-number-theory × 24
124 abstract-algebra × 51	91 calculus × 39
110 real-analysis × 42	35 graph-theory × 12
110 group-theory × 33	30 discrete-mathematics × 13
106 sequences-and-series × 33	29 polynomials × 10

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