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### Two divergent series such that their product is convergent

I faced a series question it goes something like give an example of 2 divergent series such that when the 2 series are multiplied to each other, the new series becomes convergent, although it looks ...
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### How do we integrate $xe^{x^2}$ in this differential equation?

Yeah I did try searching how to integrate $e^{x^2}$ and mostly I stumbled upon how a similar but not this function called Gaussian function $e^{-x^2}$ is un-integrable , now I was given to solve a ...
### How come it be $\frac{3}{2}A$ and not only $A$?
OK I admit I was too lazy to type this question so I took a screenshot , I got it from the site @brilliant.org where it asked in terms of $A$ what would be the 2nd summation equation ? The explained ...
### Prove that the triangles $ABC$ and $AB^{'}C^{'}$ have the same incentre.
The question is as follows if $ABC$ is a triangle, with $AD$ as the internal angle bisector of $\angle A$ with $D$ at $BC$ and $B^{'}, C^{'}$ are reflection of points $B$ and $C$ in $AD$. Show that ...