1]
     Solve

        for   . Use the natural logarithm in the solution.


SOLUTION

     

     

     

Take the natural logarithm of both sides of the equation,
according to the directions for the solution of the problem.

     



        is the final answer.




2]
     Write the first five terms of the sequence.

     


SOLUTION


     



3]
     Find the general term of the sequence, given the first four terms.

     


SOLUTION
Look at the pattern displayed by the sequence of numbers,
the way the signs alternate between plus and minus,
and notice that the numbers in the denominators are powers of 5.

     

or

     



4]
     Write the series using summation notation with the summing index  k  starting at  k=1.

     


SOLUTION
The last term in the series is, in fact, the general term of the series.
Using summation notation, we can write the series as


                               




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© edmond 2003