Adriano runs a website that writers write better stories. every month, adriano receives a subscription fee of \$5$5 from each of the subscribers to his website. the website had 200200 subscribers last month. this month 4040 new members joined the website and 1010 members cancelled their subscription. how much money will adriano's online business earn this month?

Subscription fee for a month = $ 5

Subscription fee for a writer who signs up = $ 5

Number of subscribers last month = 200

New members who joined the website = 40

Number of subscribers who left the website = 10

Hence, total subscribers in the present time =

Now, total subscription fee received this month =

Hence, the answer is $1150.

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}