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

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