Question

is arithmetic series always divergent?

Answer 1

The only convergent infinite arithmetic series is the series where all terms are zero.

You might mean an arithmetic progression / arithmetic sequence. The answer here is also no.

Answer 2

constant series converge, also.

Answer 3

arithmetic series has \(a_{n+1}= a_n + difference\)
if d =0, then \(a_{n+1}=a_n\)
for example: 1,1,1,1,.......,1
That is a arithmetic series with d =0, it converges to 1