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Evaluate the series .
\(\dfrac{1}{3^1}+\dfrac{4}{3^2}+\dfrac{7}{3^3}+\dfrac{10}{3^4}+\cdots\)

 Feb 15, 2020
 #1
avatar+302 
+1

How do we know where it ends?

 Feb 15, 2020
 #2
avatar
+1

It doesn't end, it's a infinite geometric sequence.

Guest Feb 15, 2020
 #3
avatar+302 
0

Ooh, sorry I can't help you. I haven't learned this yet...

AnimalMaster  Feb 15, 2020
 #4
avatar
+1

∑[(3n - 2) / 3^n, n, 1, ∞] = 5 /4

 Feb 15, 2020
 #5
avatar+486 
+4
Call this series S. We compare S to 1/3 S:

 

 

 

 

 

 

 

Subtracting the second equation from the first, we see that

 

 

 

 

 

 

 

 

Therefore,

 

 

 

 

 

 Feb 15, 2020
edited by SpongeBobRules24  Feb 15, 2020
 #6
avatar+108723 
0

Hi Spongebob,

Deleted,  my apologies.

 

Your answer is very interesting.

 Feb 15, 2020
edited by Melody  Feb 16, 2020
 #7
avatar+486 
+2

I tried this answer and it is correct, one of the users above got the same answer as me

 Feb 16, 2020
 #8
avatar+108723 
0

Yes, sorry, my mistake.

Melody  Feb 16, 2020
edited by Melody  Feb 16, 2020
 #9
avatar+486 
+2

It's ok, it happens to everyone.

 Feb 16, 2020

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