1. Let MATH
    1. Find the first 4 terms of this sequence.

 


 

    1. Does this sequence converge or diverge? If it converges, state the limit.



 

    1. Find $s_{4}$ where $s_{n}$ is the $n^{th}$ partial sum of the series MATH$ $You do not need to simplify your answer.

 


 

    1. Does MATH converge or diverge?

 

  1. Determine if the series MATH converges or diverges.

 

 

 

 

 


 

  1. Determine if the series MATH is absolutely convergent, conditionally convergent, or divergent.

 

 

 

 

 

 

 


 

  1. Find the radius of convergence of MATH

 

 

 

 

 


 

  1. The interval of convergence of the power series MATH is either MATHMATHMATH or MATH Determine which of these four options is correct.

 

 

 

 

 

 


 

  1. Quick calculations
    1. Find the exact value of MATH

 

 

 

 


 

    1. If $f(x)=x^{3}e^{x},$ find $f,^{prime }(2).$

 

 

 


 

    1. Find MATH

 

 

 

  1. For each set of requirements below, either give an example that fits the requirements or explain why it is impossible to do so.

1.      A divergent geometric series.

 


 

2.      A sequence $a_{n}$ so that MATH diverges and MATH converges.

 


 

3.      A sequence $a_{n}$ so that MATH and MATH diverges.