Answer:
Convergent
Step-by-step explanation:
∑₂°° 1 / (k (ln k)³)
Applying integral test:
∫₂°° 1 / (x (ln x)³) dx
If u = ln x, then du = 1/x dx.
∫ (1 / u³) du
-1 / (2u²) + C
Substitute back:
-1 / (2 (ln x)²) + C
Evaluate between the limits:
-1 / (2 (ln ∞)²) − -1 / (2 (ln 2)²)
1 / (2 (ln 2)²)
The integral converges, therefore the series must also converge.
