1. Write a program to calculate partial sums for the infinite series

    1+1/2^5+1/3^5+1/4^5+...+1/n^5+...

    (here n^5 means n to the fifth power,i.e, n times n times n times n times n). This series is convergent (by the integral test). Can you figure out what is the approximate value of its sum accurate up to six decimal places? How many terms in the sum are needed to get the desired accuracy?

    (Send the program and your comments.)

  2. Write a program to calculate partial sums for the alternating infinite series

    1-1/2^5+1/3^5-1/4^5+...+1/n^5-...

    (here n^5 means n to the fifth power, i.e, n times n times n times n times n). This series is convergent (by the Leibniz test). Can you figure out what is the approximate value of its sum accurate up to six decimal places? How many terms in the sum are needed to get the desired accuracy? How does this compare with the results of first problem? Which series converges faster?

    (Send the program and your comments.)

  3. Write a program to print a table of values of trig functions sine, cosine and tangent for angles from 0 to 90 degrees in four different columns. The beginning of the table should look like 
    Degree   Sine            Cosine          Tangent
0.       0.000000        1.000000        0.000000
1.       0.017452        0.999848        0.017455
2.       0.034899        0.999391        0.034921
.........
    Look at the results for 90 degrees and discuss the value of tangent.
E-mail your solutions to milicic@math.utah.edu. This assignment is due February 11th.