Number & Operations for Teachers
Copyright David & Cynthia Thomas, 2009
Exercises
1. Build a numerical model for the geometric series similar to that shown in Table 7.2.
n
(1/4)^n
Partial Sum
1
0.250000000
2
0.062500000
0.312500000
3
0.015625000
0.328125000
4
0.003906250
0.332031250
5
0.000976563
0.333007813
6
0.000244141
0.333251953
7
6.10352E-05
0.333312988
8
1.52588E-05
0.333328247
9
3.8147 E-06
0.333332062
10
9.53674E-07
0.333333015
Table 7.2: Numerical Model for the Geometric Series
2. The figure at the right provides a concept model for the following arithmetic series:
1 + 2 + 3 + … + n. Find an expression for the sum of this series in terms of n.
1 + 3 + 5 + 7 + 9
3. The figure at the right provides a concept model for the following arithmetic series:
13 + 23 + 33 + … + n3. Find an expression for the sum of this series in terms of n.
13 + 23 + 33