Compute (the 5th partial sum) of :

Note: if giving a decimal approximation to this part, you may need to enter more digits than usual.

Estimate the error in using as an approximation of the sum of the series (i.e. use ):
Estimate =

Use and to find a better estimate of the sum:

Note give each answer accurate to (at least) five decimal places.

You can earn partial credit on this problem.