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Similar softwareQ:

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.

A:

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.

Q:

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)

A:

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.

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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

References

External links
Autodesk page on AutoCAD

AutoCAD
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Category:Computer-aided design software for Windows
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What’s New In AutoCAD?

Create rectangular, elliptical and rounded rectangles. New rectangle geometry options offer precision and rigidity for your designs. (video: 4:37 min.)

Surface modeling allows you to incorporate complex geometry and curves, quickly and easily. (video: 2:32 min.)

Edit text in the template. You can now edit text in the template for any section of the drawing or cross section view you need to edit. (video: 1:14 min.)

Draw and edit raster images. The newest Raster Imaging feature allows you to quickly incorporate raster images such as a watermark into your drawings. (video: 1:02 min.)

Add precise measurement data to your drawings. New features include the ability to embed text, coordinates, dimensions, angles and arrowheads. (video: 2:43 min.)

Stay on the most recent page in a chapter of a reference manual. With the new bookmarking feature, you can place a reference page on your screen and quickly return to it when needed. (video: 2:27 min.)

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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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