For example, it can symbolically compute series, such as
sage: sum((1)/(n^4),n,1,Infinity)
1/90*pi^4
There is a very nice introduction on the CUNYMath Blog, that goes over a few of the basics. For a longer intro, there are tons of tutorial on the SageMath website. And for people wanting to learn calculus and/or Sage, the Smith College has a page on Calculus in Context.
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