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Prove $\sum_{k=1}^{n} \left(\dfrac{1}{k} – \dfrac{1}{n+k}\right) = \log n – \log\log n + O\left(\frac{1}{\log n}\right)$

I’m trying to prove the following problem:

How do I prove the following:

Thanks for all the help.


Write $\frac{1}{k} – \frac{1}{n+k}$ as $\frac{1}{n+k-k} – \frac{1}{k}$, then sum the two terms.
You will get an expression of the form $\sum_{k=1}^n k^{ -2}-\sum_{k=1}^n k^{ -1} = \sum_{k=1}^n k^{ -2} – \frac{1}{n}\sum_{k=1}^n k^{ -1}$.
Then it is not hard to evaluate this sum.


How do I get a Scala’s map to retain the order of the first argument list passed to map?

The following code
import scala.collection.JavaConversions._

val A = Map(“k” -> 1)
val B = Map(“l” -> 1)
val C = Map(“i” -> 1)

println(B ++ A ++ C)

prints the following:
Map(l -> 1, i -> 1, k -> 1)

This doesn’t make any sense to me, why does it do this? It should print:
Map(l -> 1, i -> 1, k -> 1)


The default ordering of the keys of the returned map is consistent with the order of the order of the map being created.
In the case of the code you pasted it does not make much sense to create three maps where k, l and i are the keys of each.

Erratum to: Global Health Action 8(3) DOI 10.1186/s12939-017-0607-2 {#Sec1}

After publication of the original article \[[@CR1]\], it was noticed that the publication date for the article (11 March

AutoCAD 2019 23.0 Free [32|64bit]

In the last two decades Autodesk has developed a file format, exchange format, that supports separate coordinate systems, feature classes, and free-hand drawing with no specific object functionality.

Since 2016, Autodesk has also developed a set of APIs for users to create and design for the Internet of Things. These are:
Autodesk IoT Core Autodesk IoT Edge

See also
Architectural design automation
List of applications with iCAD


External links
Autodesk page on AutoCAD

Category:Computer-aided design software
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AutoCAD 2019 23.0 Crack

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In our last update, we announced the availability of new features in AutoCAD 2020 that make creating, editing and managing model design, and task-based BIM workflows more efficient. Today, we’re announcing some more exciting updates for AutoCAD that will further streamline the design and implementation of engineering projects and workflows.We’re also announcing the availability of a new template for AutoCAD users who need to create bill of materials (BOM) documents. While many of these features are available in other programs like AutoCAD LT, they’re not typically included at the Autodesk Exchange that design and architectural professionals use to manage their projects. Our goal is to make the Exchange even better and bring these features to the Exchange community.Let’s begin by taking a look at a few features in AutoCAD 2023 that give you a better experience while you work with 2D objects.We’ve made the transition to DXF and DWG files, a popular and established industry format, even easier for you. The new DXF and DWG import and export features are helpful for all levels of users, including CAD and BIM managers. The workflow for using these files is also enhanced, with more intuitive window

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2 GB available hard disk space
Graphic card: 2 GB DDR2 or higher
Mouse or Touchpad
Internet access
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