Mathematics, as we all know, is bestowed with tremendous beauty. Unfortunately, unlike other forms of art, mathematical beauty is not easily manifested to general audience. One has to work upon it for some time in order to have a natural appreciation for its sublime magnificence. Many mathematical expressions often exercise their fascination to us. One such expression that I've tried digging deeper is: \[\Large\left(x+\frac 1 x\right)\] I didn't find a name assigned to this form in mathematical literature; so i called them the "madness sum" in my first problem, and stuck with it later. I've tried hard to go far from the books' level into the realms of its opportunities and hopefully came up with some of the good results.
In the note that I'm going to share below you'd find some problems regarding the madness sum. I would further add some more problems as new insights come. Thanks.
Click here for the note: The Madness sum