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

b.) 160 miles on a 5 gallons car

step-by-step explanation:

240/10=24 miles/gallon

160/5=32 miles/gallon

30/1=30 miles/gallon

168/6= 28 miles/gallon

32 miles/gallon is the most amount, so this is the best.

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