Introducing another Wolphram calculator, reworked slightly by me.
This toy below is used to calculate the sum of series (not only numerical, but also functional!):
It works straightforwardly, in the “Series” field we enter the general word of the series, in the “From” field the beginning of the index (what is at the bottom in the sigma sign of the series), in the “To” field the end of the index. By default we count infinite series, so we leave infinites, but with the calculator we will also count finite series, in which case we would enter, for example, 100 there.
Of course, the calculator will also serve us well for typical “check if the series converges” type tasks. We simply count the sum of the series with a calculator and if a finite number comes out, it means that the series converges. If the series diverges, the calculator itself will tell us this through the message “does not converge”.
Example
Let’s examine the sum of the series:
We enter the appropriate values into the calculator:
, click on ‘Calculate’ and have the result:
The sum of the series is the number: 
, approximately 0.384948. Of course, it follows that it is convergent. As a bonus, at the bottom we have several representations of this number by other ranks.
I’m sure that this calculator will be a super help for everyone counting series (you can easily check the result).
As always, I invite your questions and comments below the post!
