Use the ratio or root test to check if the series converges

Converges

Step-by-step explanation:

n = k+1

(k+1) ÷ [ln(k+1)]^(k+1)

n = k

k ÷ [ln(k)]^k

{(k+1) ÷ [ln(k+1)]^(k+1)} ÷ {k ÷ [ln(k)]^k}

= {(k+1)/k} × {[ln(k)]^k}/{[ln(k+1)]^(k+1)}

{[ln(k)]^k}/{[ln(k+1)]^(k+1)} is decreasing at a much faster rate than the rate of increase of {(k+1)/k}.

Therefore the product is less than 1.

Hence it converges

answer: the first one

step-by-step explanation: use a calculator and divide the minutes by the dollars.