Use the integral test to determine if the series the summation from k equals 1 to infinity of the quotient of 1 and the product of k and the 3rd power of the natural log of k...

Question

Use the integral test to determine if the series  is convergent or divergent. Make sure that you set up the problem correctly and use the proper notation.

Answer 1

The integral is -1/(2 (ln(k))^2) + C; -1/(2 ln^2(k)) has a limit of 0 as x goes to infinity. Note the negative sign; this assures us that the integral will be positive.

Thus, the sum converges.