Question

Does the series converge or diverge? If it converges, what is the sum?

Answer 1

hate these questions so much, i can make no sense of it

Answer 2

hint: what is your r value?

Answer 3

-4?

Answer 4

not quite

you have the series

a*(r)^(n-1)

Answer 5

so if

a*(r)^(n-1) = -4(-1/2)^(n-1)

what is r?

Answer 6

(remember, r is the number that the exponent "belongs" to)

Answer 7

-1/2

Answer 8

good

since r is between -1 and 1, the series converges

Answer 9

now, it also asks for the sum

Answer 10

the sum = a/(1-r) = ?

Answer 11

what is a

Answer 12

a*(r)^(n-1) = -4(-1/2)^(n-1)

what does a = ?

Answer 13

oh -4 duh

Answer 14

good

Answer 15

so 1/1-1/2? how do you do that

Answer 16

a/(1-r) = ?

Answer 17

wasnt r 1/2? so how do you put 1/2 in a demoninator

Answer 18

what is 1 - (-1/2)?

Answer 19

1 1/2 because its minus a negative which is really plu s

Answer 20

good, we can rewrite that as 3/2

Answer 21

what is -4/(3/2) ?

Answer 22

im not sure

Answer 23

remember your rules for dividing fractions

Answer 24

flip the second fraction and then multiply

Answer 25

-4 * (2/3) = ?

Answer 26

6/3 ???

Answer 27

what is -4 * 2?

Answer 28

oh

Answer 29

8/3

Answer 30

-8/3

Answer 31

so -8/3 is your answer

Answer 32

okay thank you