Mason is going to have a lemonade stand. his aunt buys him 10 lbs. of lemons. if he sells each cup for a quarter, how many cups does he need to sell to pay her back?
the price of 1 lb. of lemons is $0.89.
i have already did 0.89 x 10 which gives me 8.90.

8.90 divided by 0.25= 35.6 (round up to 36 because you cant sell .6 cups of lemonade)

he would have to sell 36 cups of lemonade to pay his aunt back

after he sells 36 cups and pays his aunt back the $8.90 he will have $0.10 left to keep for himself

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}