Plot of Monthly Stockpile for the
First Six Months

The Plot of the Partial Sum S_n
nersus n

Based on the stockpile data on the left, it is noted that the sum of the stockpiles follows the following trend and can be represented by the series:

where n represents the month (i.e., n = 1 is January, n = 2 is February and so on). It is also recognized that this series is alternating harmonic series.

To determine if the warehouse is suitable or not in long run, the partial sum of the series for n = 12 is obtained as an approximation:

Since the warehouse is 65.3% occupied by the end of a year, which is a little more than half, the warehouse is considered suitable for a long period of time.

The error involved in using the partial sum as an approximation for the total sum is given by:

     

The partial sums for the first 12 terms are shown in the figure to show the convergence of the series.