8.37.3 Can you answer these questions?

8.37.3.1 Mathematica incorrectly claims an infinite sum doesn't converge

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=276095

When I compare the output of the following commands I get contradictory results: 
 Sum[BesselJ[k, 1], {k, 0, Infinity}] 
NSum[BesselJ[k, 1], {k, 0, Infinity}] 
 
The ... 
[numerics] [warning-messages] [summation]
 

asked by Chris https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=67334 Score of 1

8.37.3.2 SortBy the second element in the sublists

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=276010

Is there a way to sort sublists in a list by the sublists' second element? 
For example, if the list is: 
... 
[list-manipulation] [sorting]
 

asked by Y. zeng https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=80680 Score of 1

8.37.3.3 The derivative anomaly in Mathematica 13, showing in the Plot[] function

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=276070

Edit: 
Still inexplicably, it was found that in the  Plot[]  functions, showing a correct curve plot for the expression computing the derivative incorrectly, when '... 
[calculus-and-analysis]
 

asked by ghogoh https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=45695 Score of 1

answered by azerbajdzan https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=53172 Score of 0