Question

Prove $x_n = \sum_{k=1}^n \frac{1}{(a+(k-1)\cdot d)\cdot(a+k\cdot d)}$ is a bounded sequence.

score 35 · Answer 1 · 2026-03-25 03:03:55

35

Views

Prove $x_n = \sum_{k=1}^n \frac{1}{(a+(k-1)\cdot d)\cdot(a+k\cdot d)}$ is a bounded sequence.

Published on 25 Mar 2026 - 3:03

score 39 · Answer 2 · 2018-10-22 18:54:45

39

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Showing that $ O \cap M = \emptyset $ or $ O \cap M = \{b\} $ Where $M$ is a set and $O$ is the set of Upper Bounds.

Published on 22 Oct 2018 - 18:54

score 225 · Answer 3 · 2026-03-25 17:20:57

225

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Infimum and supremum of $x^5y^2z$

Published on 25 Mar 2026 - 17:20

score 46 · Answer 4 · 2018-10-23 16:27:30

46

Views

How to interpret this notation

Published on 23 Oct 2018 - 16:27

score 72 · Answer 5 · 2018-10-25 18:22:31

72

Views

Validate the proof that $x_n = {\ln n \over n}$ is bounded by $\ln2$ and find $\sup\{x_n\}$

Published on 25 Oct 2018 - 18:22

score 152 · Answer 6 · 2018-10-25 19:22:34

152

Views

What is exactly meant with $\int f d\mu=\sup_{\rho \in \Phi^{+}_{f}}\int\rho d\mu$? Why supremum?

Published on 25 Oct 2018 - 19:22

score 900 · Answer 7 · 2018-10-25 22:52:08

900

Views

When is the supremum of one set equal to the infimum of another set?

Published on 25 Oct 2018 - 22:52

score 1.1k · Answer 8 · 2018-10-26 19:49:18

1.1k

Views

When are the suprema of two sets equal?

Published on 26 Oct 2018 - 19:49

score 58 · Answer 9 · 2018-10-27 18:23:10

58

Views

Proof of $sup\bigcup_{i\in I} A_{i}=sup\{supA_{i}, i\in I\} $

Published on 27 Oct 2018 - 18:23

score 283 · Answer 10 · 2018-10-28 09:16:32

283

Views

General topology / real analysis - Suppose $S$ is a bounded and closed nonempty subset of real numbers. Prove sup S is in S

Published on 28 Oct 2018 - 9:16

score 73 · Answer 11 · 2018-10-28 09:52:58

73

Views

Supremum of $\frac{(x+y)^{2}}{2^{xy}}$

Published on 28 Oct 2018 - 9:52

score 94 · Answer 12 · 2018-10-29 13:25:42

94

Views

Continuity of the following function

Published on 29 Oct 2018 - 13:25

score 384 · Answer 13 · 2018-10-29 23:06:40

384

Views

supA and infA, if $A:=\{\frac {a+b+c}{abc}: a,b,c \in \Bbb N\}$

Published on 29 Oct 2018 - 23:06

score 46 · Answer 14 · 2018-11-01 16:25:00

46

Views

proof verification for $A_n\uparrow A \implies A-A_n\downarrow \emptyset$

Published on 01 Nov 2018 - 16:25

score 112 · Answer 15 · 2026-03-25 19:07:15

112

Views

The reasoning behind $\sup\{\alpha\beta+\alpha\zeta\mid\zeta<\gamma\}=\alpha\beta+\sup\{\alpha\zeta\mid\zeta<\gamma\}$

Published on 25 Mar 2026 - 19:07

List Question

Prove $x_n = \sum_{k=1}^n \frac{1}{(a+(k-1)\cdot d)\cdot(a+k\cdot d)}$ is a bounded sequence.

Showing that $ O \cap M = \emptyset $ or $ O \cap M = \{b\} $ Where $M$ is a set and $O$ is the set of Upper Bounds.

Infimum and supremum of $x^5y^2z$

How to interpret this notation

Validate the proof that $x_n = {\ln n \over n}$ is bounded by $\ln2$ and find $\sup\{x_n\}$

What is exactly meant with $\int f d\mu=\sup_{\rho \in \Phi^{+}_{f}}\int\rho d\mu$? Why supremum?

When is the supremum of one set equal to the infimum of another set?

When are the suprema of two sets equal?

Proof of $sup\bigcup_{i\in I} A_{i}=sup\{supA_{i}, i\in I\} $

General topology / real analysis - Suppose $S$ is a bounded and closed nonempty subset of real numbers. Prove sup S is in S

Supremum of $\frac{(x+y)^{2}}{2^{xy}}$

Continuity of the following function

supA and infA, if $A:=\{\frac {a+b+c}{abc}: a,b,c \in \Bbb N\}$

proof verification for $A_n\uparrow A \implies A-A_n\downarrow \emptyset$

The reasoning behind $\sup\{\alpha\beta+\alpha\zeta\mid\zeta<\gamma\}=\alpha\beta+\sup\{\alpha\zeta\mid\zeta<\gamma\}$

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