To add 20.4 + 3.75 + 4.25, Crystal first added 3.75 and 4.25. Which property did Crystal use to add mentally? A. Associative Property of Addition
B. Commutative Property of Addition
C. Distributive Property
D. Identity Property of Addition

Associative Property of Addition

Step-by-step explanation:

From the list of given options, option A correctly answers the question and this is because

--- (1)

or

--- (2)

The above illustrations only apply to Associative Property of Addition

In Crystal's case:

This can be compared to (1) above

Hence;

Option A answers the question

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}