Question

if c is a positive real number and ak=klnc, for what values of c, if any, does the infinite series ?k=1?ak converge?

Answer 1

Consider lim[klnc] where k tends to ∞. Clearly, the result is ∞ since lim[k] where k tends to ∞ is ∞.

By divergence test, there is no such c.