哪种编程语言或库可以处理无限系列？ [英] Which programming language or a library can process Infinite Series?

问题描述

哪种编程语言或库能够处理无限级数（如几何或谐波）？它可能必须拥有一些知名系列的数据库，并在收敛的情况下自动给出适当的值，并且可能在发散情况下产生异常。

例如，在Python中，它可能如下所示：

  sum = 0 
 sign = -1.0 
 （1，Infinity，2）：
 sign =  -  
 $ + $ sign $ / $ $ b 
然后，sum必须是math.pi / 4，而不在循环中进行任何计算（因为它是一个众所周知的总和）。 
 
解决方案
你需要一些可以做象征性计算的东西，比如 Mathematica 。 
您也可以考虑quering  wolframaplha：sum（（ -  1）^ i * 1 / i，i，1，inf）  
Which programming language or a library is able to process infinite series (like geometric or harmonic)? It perhaps must have a database of some well-known series and automatically give proper values in case of convergence, and maybe generate an exception in case of divergence.

For example, in Python it could look like:
sum  = 0
sign = -1.0
for i in range(1,Infinity,2):
     sign = -sign
     sum += sign / i
then, sum must be math.pi/4 without doing any computations in the loop (because it's a well-known sum).
解决方案
You need something that can do a symbolic computation like Mathematica.
You can also consider quering wolframaplha: sum((-1)^i*1/i, i, 1 , inf)

                        
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