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!!

#Combinatorics

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$