Plot of Monthly Stockpile for the
First Six Months
Table: Partial Sum of the
Series
(n =12)
n

S_{n}

1

1

2

0.5

3

0.8333

4

0.5833

5

0.7833

6

0.6167

7

0.7595

8

0.6345

9

0.7456

10

0.6456

11

0.7365

12

0.6532

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. 