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I only know how to prove limits of sequences not series:(

what a cool series though..

yep!! this is very interesting!!

god we really dont know what we have on our hands with this math stuff.

you missed the sum. the approach is +ve ... BRB in 3 hrs

And you can use a geometric series from there to get \(\displaystyle \frac{e^{-1}}{1-e^{-1}}\)

change of limits on the sum is the trick!!

sorry.. what do we call that ... k ... counter as in loop

Are you allowed to take the limit through the sum, as I have done?

this is equivalent to
lim n->inf (1 - 1/n)^n + (1 - 2/n)^n + (1 - 3/n)^n + ....

let's put a new counter
m = N - k + 1 <-- this counts from opposite.

Yeah, that's what I did too. I didn't know it was called a counter, though.

i don't know what it is called either ... may be some incremental variable.

in programming ... in loop ... it's called counter... :D

lol

gotta go ... bye