Let $sum_{n=1}^{infty }x_{n}$ a convergent series of positive real numbers. Show that $inf(lim) nx_{n}=0$

I don’t really know if it is just some theorem, but please help, I have no clue on these subjects, thanks

magento2 – Magento 2: How to show custom customer attribute value in an order report in the admin

I am trying to create a custom order report to show some customer information along with the order details. I have created few custom attributes for Customer. The report is very similar to the default Magento report Magento/Sales/Model/ResourceModel/Report/Invoiced/Collection/Order.php. But I need to join the custom customer attributes to this report.

I have an attribute named my_custom_customer_attribute and it has got some value for a particular customer. When I generate an order report, I need to show this value along with the order number, customer name, order total and “my_custom_customer_attribute`. I am extending the above Order report. So I need a way to join the custom attribute to the Collection.

Please could someone point me in the right direction.

Thanks

How do I get GitHub to not show organization’s updates on my timeline

I was recently added to an organization on GitHub and consequently, and updates that anyone makes to a repository on the organization are displayed on my timeline. Is there any way to suppress these updates?

html – SVG doesn´t show up

this is the HTML code:

<html>
<head>
    <title>HOME | index</title>
    <meta charset="utf-8"/>
    <meta name="viewport" content="width-device-width, initial-scale=1.0">
    <!-- <link rel="stylesheet" type="text/css" href="style.css"> -->
</head>
<body>                       
    <div style="text-align:center;padding:150px 0;">
        <object type="image/svg+xml" data="/img/menu.svg">
            <!-- <embed src="/img/menu.svg"> -->
        </object>
    </div>                
</body>

And this is the SVG:

<svg version="1.1" id="menu" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px"
         viewBox="0 0 228.4 18.2" style="enable-background:new 0 0 228.4 18.2;" xml:space="preserve" width="500px" height="500px">
    <style type="text/css">
        .st0{
            fill:none;stroke:#000000;stroke-width:10;stroke-miterlimit:10;
        }
    </style>
    <line id="XMLID_1_" class="st0" x1="5.8" y1="10" x2="221.8" y2="10"/>
</svg>

Same result if I use embed src.
The SVG is just a stroke, and doesn’t show up with any browsers (firefox, chrome, edge). I am new with SVG images.

sharepoint online – How I can show the user-names for a People or Group site column which allow multiple selection inside our PowerBi report

After you have added the List into Power BI use Power Query Editor (the ellipses on the table and then select edit query) and find the column in question.

As you see below there is a MemberId Column in my example which contains a List value.

enter image description here

Select the Double Arrows and then select Expand to New Rows.
enter image description here

You should see a result where each member of the group gets their own row in the table.

enter image description here

It will come out with the User ID but you should be able to link this the same as you did with point 1.

group theory – Show $(Gtimes H)/(Ktimes K’) cong G/Ktimes H/K’$ if $Klhd G$ and $K’lhd H$

As the title says, I want to show that $(Gtimes H)/(Ktimes K’) cong G/Ktimes H/K’$ if $Klhd G$ and $K’lhd H$.

I already showed that $Ktimes K’$ is a normal subgroup of $Gtimes H$ and I think that I should use the isomorphism theorem stating that if $A,B$ are groups and $f:Ato B$ is a homomorphism then $f(A)=A/text{ker}(f)$. But I can’t figure out how to go further. Can you help me to prove this problem?

is it possible to add json code to hide and show other rows based on column value?

am using view formatting with json wondering if its possible to add
button that can sort , hide and show other rows based on their column value, like only show items in toys department store and hide other departments sports etc

discrete mathematics – Show that $dfrac{(2n)!}{2^{2n}(n!)^2}$ is asymptotically equivalent to $dfrac{1}{sqrt{pi n}}$

Problem

Show that $dfrac{(2n)!}{2^{2n}(n!)^2}$ is asymptotically equivalent to $dfrac{1}{sqrt{pi n}}$.

Can someone please verify my solution attempt?

Solution

Given functions $f(n)$ and $g(n)$, $f(n)$ is asymptotically equivalent to $g(n)$ if and only if:

$$lim_{ntoinfty}dfrac{f(n)}{g(n)}=1.$$

Let $f(n)=dfrac{(2n)!}{2^{2n}(n!)^2}$ and $g(n)=dfrac{1}{sqrt{pi n}}$.

By Stirling’s formula, $n!$ can be expressed as:

$$n!=sqrt{2pi n}left(dfrac{n}{e}right)^n e^{epsilon(n)}$$

where

$$dfrac{1}{12n+1}leqepsilon(n)leqdfrac{1}{12n}.$$

So, $f(n)$ may be rewritten as:

$$begin{aligned}
f(n)&=dfrac{(2n)!}{2^{2n}(n!)^2}\
&=dfrac{sqrt{4pi n}left(dfrac{2n}{e}right)^{2n} e^{epsilon(2n)}}
{2^{2n} 2pi nleft(dfrac{n}{e}right)^{2n} e^{2epsilon(n)}}\
&=dfrac{2^{2n+1}left(dfrac{n}{e}right)^{2n} e^{epsilon(2n)}}
{2^{2n+1} sqrt{pi n}left(dfrac{n}{e}right)^{2n} e^{2epsilon(n)}}\
&=dfrac{e^{epsilon(2n)}}{ e^{2epsilon(n)}sqrt{pi n}}
end{aligned}$$

So, since both $epsilon(n)$ and $epsilon(2n)$ approach $0$ as $ntoinfty$, we have:

$$lim_{ntoinfty}dfrac{f(n)}{g(n)} = lim_{ntoinfty} left(dfrac{e^{epsilon(2n)}}{ e^{2epsilon(n)}sqrt{pi n}} cdot sqrt{pi n}right)=lim_{ntoinfty} dfrac{e^{epsilon(2n)}}{ e^{2epsilon(n)}}=dfrac{lim_{ntoinfty}e^{epsilon(2n)}}{lim_{ntoinfty}e^{2epsilon(n)}}=1,$$

as required.

GitHub: not show organization’s updates on my timeline

I was recently added to an organization on GitHub and consequently, and updates that anyone makes to a repository on the organization are displayed on my timeline. Is there any way to suppress these updates?

Why transaction shows in received but does not show in balances

I had a transaction sent while the Bitcoin Core was syncing. Now the transaction shows up in the received transactions but there is no balance.

Is it possible to recover the coin so I can move it to a different wallet.