Question

ind the sum of the following infinite geometric series, if it exists.
2 + 6 + 18 + 54 +…

Answer 1

@nincompoop

Answer 2

25,982

Does not exist

23,567

29,034

Answer 3

What is the common ratio here ?

Answer 4

dont know that

Answer 5

Can you determine the pattern here,

2,6,18,54,... ?

Answer 6

add 12

Answer 7

Nope, as 18 + 20 is not equal to 54.

See, they are being multiplied by 3.

Answer 8

ok right!

Answer 9

Right?

Answer 10

3>1 thus dne

Answer 11

The sum would only exist if the value of r were less than 1. The r here is 3.

Answer 12

Good. So, common ratio is 3.

Now, formula for sum of infinite geometric series is a/(1-r)

where r is common ratio and a is the first term

First term is 2

common ratio is 3

so sum = 2/(1-3) = -1

(Thus does not exist as the sum is not negative here)

Answer 13

we already know the ratio is 3

Answer 14

a_i/a_j <1 for all I = j+1
this is necessary for convergence

Answer 15

i = j + 1

Answer 16

The tricks are already mentioned above by @zz0ck3r and @NoelGreco .

Answer 17

ohhhh ok so the correct answer would be is does not exist

Answer 18

Got it @chocodropa7 ?

Answer 19

Yes.

Answer 20

Got IT!

Answer 21

correct

Answer 22

thank you

Answer 23

You're welcome choco. Best of Luck

Answer 24

Oh sorry @mathslover my tablet is hard to read and I did not know you were walking him through it.

Answer 25

http://www.regentsprep.org/Regents/math/algtrig/ATP2/ArithSeq.htm

Answer 26

:) No problem zzr0ck3r :) Its fine and even good to see.