Reduce the fraction to lowest terms. Do not us
- 5jk/35j2k2

Step-by-step explanation:

(Interpreting equation as)

We can reduce the fraction by dividing the top and the bottom by terms they have in common.

First, lets rewrite both the numerator and denominator in terms of each other.

If you expand the fraction, you will get exactly what you start with, now this is fine.

As we can see both halves of the fraction have a common term (), so we can divide by this - and the fraction will still be equivalent to as it was before

, or simplified further,

I'm glad you asked!

Step-by-step explanation:

=

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step-by-step explanati∵∵∴∴on:

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}