
(a)
Make a table of the partial sums of the series for
(a)

Answer to Problem 71PPS
Explanation of Solution
Given:
Consider
Make a table of the partial sums of the series for
Concept Used:
Substitute k = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 in the expression
Calculation:
Make a table of the partial sums of the series for
1 | 4 |
2 | 10 |
3 | 18 |
4 | 28 |
5 | 40 |
6 | 54 |
7 | 70 |
8 | 88 |
9 | 108 |
10 | 130 |
(b)
Graph ( k , partial sum)
(b)

Explanation of Solution
Given:
Consider
Concept Used:
Graph k as x − axis and partial sum as y − axis.
Calculation:
Graph the k (number of terms) and the partial sum.
(c)
Graph
(c)

Explanation of Solution
Given:
Graph
Concept Used:
Graph the quadratic function
Calculation:
Table for graphing for
| Graph of |
(d)
Find the similarity of two graphs.
(d)

Answer to Problem 71PPS
Explanation of Solution
Given:
What do you notice about the two graphs?
Consider
Concept Used:
The graphs cover the same range. The domain of the series is the natural numbers, while the domain of the quadratic function is all real numbers,
(e)
What conclusions can you make about the relationship between quadratic function and the sum of arithmetic series?
(e)

Answer to Problem 71PPS
Explanation of Solution
Given:
What conclusions can you make about the relationship between quadratic function and the sum of arithmetic series?
Concept Used:
For every partial sum of an arithmetic series, there is a corresponding quadratic function that shares the same range,
(f)
Find the arithmetic series that relates to
(f)

Explanation of Solution
Given:
Find the arithmetic series that relates to
Concept Used:
The arithmetic series is
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