First, rewrite 16/25 and 13/20 so that they have a common denominator.

The answer to your question is 64/100 and 65/100

Step-by-step explanation:

Data

Common denominator of   16/25 and 13/20

Process

1.- Find the least common factor of 25 and 20.

                            25      20      2

                            25      10       2

                            25        5       5

                              5         1       5

                               1

   L.C.F. = 2 x 2 x 5 x 5 = 100

2.- Convert each fraction to the denominator 100

           100 / 25 = 4

            16/25 = (16 x 4) / 100

                     = 64/100

            100 / 20 = 5

            13/20 = (13 x 5)/100

                      = 65/100  

Step-by-step explanation:

List of multiples of 25: 0, 25, 50, 75, 100, 125, 150, ...

List of multiples of 20: 0, 20, 40, 60, 80, 100, 120, 140, ...

LCM(25, 20) = 100

100 = (25)(4)

100 = (20)(5)

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}

you didn't give me the choices, so i will just give you the graph so you can look at your choices and choose the right one.