Your class hopes to collect at least 325 cans of food for the annual food drive. there were 135 cans donated the first week and 89 more the second week. write an inequality that describes this situation. let c represent the number of cans of food that must be collected by the end of the third week for your class to meet or surpass your goal. how many cans are needed to meet or surpass your goal? 135 + 89 + c ³ 325; c ³ 101 135 + 89 + 325 ³ c; c ³ 549 135 + 89 + c ³ 325; c £ 549 135 + 89 + c > 325; c > 101

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}

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