Question 1208710
<pre>

I think this is a trick question and one such arithmetic series 
could be:

{{{1/30375+1/30375+1/30375+""*""*""*""}}} to 30375 terms 

with common difference d=0. It has a sum = 1 which is the 
smallest positive perfect 5th power.

There are other arithmetic series with 30375 terms and 
sum 1 with tiny first terms and tiny common differences 
greater than 0, but I see no reason the common difference 
can't be 0.
 
Edwin</pre>