Question

Will fan!

Answer 1

Like what dear?

Answer 2

https://imgbomb.com/i/?KZVdx

Answer 3

All of these seem to have an infinite sum

Answer 4

I need to find which of these equations is a convergent series

Answer 5

Hrmm Im not actually sure :#

Answer 6

each series is a geometric series. Hopefully you agree with that statement and see why?

Answer 7

sorry C isn't geometric

Answer 8

Isnt C arithmetic?

Answer 9

yes it is, my bad

Answer 10

I need to find which one of these is a convergent series.

Answer 11

the three trailing dots imply that the series goes on forever

Answer 12

I know

Answer 13

with geometric series, the infinite series only converges if and only if |r| < 1

Answer 14

Yes but the ratio for all of them except a have a ratio greater then 1 for me

Answer 15

for example, B will not converge because r = 3 in this case and r = 3 makes |r| < 1 false

Answer 16

B will keep growing and growing. The sum won't converge to a fixed number

Answer 17

Thats what I'm thinking for all the equations

Answer 18

for c d= -0.5 and arithmetics go on forever

Answer 19

what is the value of r for choice A?

Answer 20

r = \[-\sqrt{2}\]

Answer 21

I think thats convergent but not sure

Answer 22

correct r value, but it doesn't converge since r = -sqrt(2) = -1.414 approx

r = -1.414 makes |r| < 1 false

ie, r = -1.414 is more than 1 unit away from 0 on the number line

Answer 23

A will grow forever just like B does, just at a slower pace

Answer 24

None of these equations converge then?

Answer 25

what's the r value for E ?

Answer 26

r = 2

Answer 27

so E diverges

Answer 28

what's the r value of D ?

Answer 29

d = -12

Answer 30

Wait...

Answer 31

no it's not arithmetic

Answer 32

I was thinking that

Answer 33

OH.... r = 3/4 so it is convergent

Answer 34

yep r = 0.75 makes |r| < 1 true

since it's between r = -1 and r = 1

Answer 35

Thank you so much!

Answer 36

no problem