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# Binomial Theorem?

Hello guys....

I'm back with a bang,..... I suppose ;)

Veering away from one of those "Find the number of rational terms in the expansion of..." problems a thought crossed my head and I wish it never had. Well, here goes.

Consider the expansion of $$\displaystyle (\sum _{ r=1 }^{ n }{r^{\frac{1}{r}}})^{n!}$$ (Take a breath)

Could you wonderful human beings tell me how many rational terms would be in this expansion?

I'll treat myself to an ice-cream if @Deeparaj gives the solution!

Also any new CMI students, please give a first-hand review!!! Cheers!!

Note by Anirudh Chandramouli
9 months, 3 weeks ago