I cant find an example of this series, could I get some help please?

Question

1. Consider the series
2. Use the integral test to show that this series converges.
3. Use your calculator to approximate S₁₅ for this series. You must show what you enter into the calculator.
4. Use the integral remainder theorem to determine the value n, so that S_n approximates S to within 0.0001. I want the smallest such n. You can find this value by guessing. Show your work.

Answer 1

a) Integral test will not work as integration results in a form that is identical to the original problem. However, the ratio test shows convergence.

b) S15 = 18e^-4.5 =.1999