anonymous
  • anonymous
ind the sum of the following infinite geometric series, if it exists. 2 + 6 + 18 + 54 +…
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
@nincompoop
anonymous
  • anonymous
25,982 Does not exist 23,567 29,034
mathslover
  • mathslover
What is the common ratio here ?

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More answers

anonymous
  • anonymous
dont know that
mathslover
  • mathslover
Can you determine the pattern here, 2,6,18,54,... ?
anonymous
  • anonymous
add 12
mathslover
  • mathslover
Nope, as 18 + 20 is not equal to 54. See, they are being multiplied by 3.
anonymous
  • anonymous
ok right!
mathslover
  • mathslover
Right?
zzr0ck3r
  • zzr0ck3r
3>1 thus dne
NoelGreco
  • NoelGreco
The sum would only exist if the value of r were less than 1. The r here is 3.
mathslover
  • mathslover
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)
anonymous
  • anonymous
we already know the ratio is 3
zzr0ck3r
  • zzr0ck3r
a_i/a_j <1 for all I = j+1 this is necessary for convergence
zzr0ck3r
  • zzr0ck3r
i = j + 1
mathslover
  • mathslover
The tricks are already mentioned above by @zz0ck3r and @NoelGreco .
anonymous
  • anonymous
ohhhh ok so the correct answer would be is does not exist
mathslover
  • mathslover
Got it @chocodropa7 ?
mathslover
  • mathslover
Yes.
anonymous
  • anonymous
Got IT!
zzr0ck3r
  • zzr0ck3r
correct
anonymous
  • anonymous
thank you
mathslover
  • mathslover
You're welcome choco. Best of Luck
zzr0ck3r
  • zzr0ck3r
Oh sorry @mathslover my tablet is hard to read and I did not know you were walking him through it.
nincompoop
  • nincompoop
http://www.regentsprep.org/Regents/math/algtrig/ATP2/ArithSeq.htm
mathslover
  • mathslover
:) No problem zzr0ck3r :) Its fine and even good to see.

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