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limit of sequence

given this sequence

i tried the following:

  s,n = var('s,n')
  s = sum((3*n)/sqrt(2*n^4-k^2*n^2), k, 1, n)
  s.limit(n=Infinity)

but i get:

3*limit(n*sum(1/sqrt(-k^2*n^2 + 2*n^4), k, 1, n), n, +Infinity)

which is not the result i want, this sequence either diverges or converges, so its either a number or infinity/-infinity, any ideas how to make this work properly? or can sagemath not handle this type of limits?

thank you