Question 1184295
If what you meant was

{{{lim(r-> infinity, (1+2+3+4+5+"..."+r)/"r!")}}}

then the answer is {{{lim(r->infinity, (r(r+1))/(2*"r!"))= lim(r->infinity, (r+1)/(2*"(r-1)!"))=0}}}, for {{{r >= 2}}}.

In this website you will only get a precise answer if 

you posted a precise question.

So as a piece of advice, next time, if you want tutors here 

to help you, try to be more accurate in your statement of

the problem.