Determine whether the sequence {a(n)} converges or diverges when?

Question

a(n)= 1 * 4* 9 ....(5n-1) / ((5n)^n) and if it converges, find its limit

Answer 1

I'm not sure I understand the question.

Is the numerator the product from k = 1 to n of (5k - 1)? (If so, where did the initial 1 come from; if not, please repost with the correct formula)

If so, then:

a(n) = product from k = 1 to n of (5k-1)/(5n)

Since (5k-1) is less than 5n for all k <= n, a(n) is a product of n factors all less than 1 and greater than 0.

This means that 0 < a(n) <= 4/(5n)