a(n)= 1+ (-6/ 5pi)^n what is the limit when it is convergent?

Answer 1

It is not convergent.
-6/(5pi) is less than 1, so the limit as n goes to infinity of (6/(5pi))^n is 0.

Therefore the limit as n goes to infinity of 1+(-6/(5pi))^n is 1+0 = 1.
Since the limit does not equal zero, it diverges.

Answer 2

If this is a sequence, as Ms Math has shown, the limit is 1, so it is convergent. If this is a series, then as Ms Math has stated, the series diverges because the n-th term does not have limit 0.