Write in Sigma Notation: 1/3, 2/9, -7/27, 14/81, -23/243, 34/729,...

[wow4201]

Sorry about the the markups.
This question is confusing the crap out of me.

Anyone care to help?
I see that the denominator is 3^n and there's a pattern on the numerator where a number is being added and going up by two each step.

Also not an alternating negative, since 1/3 isn't -

 

[mmm4444bot]

not an alternating negative, since 1/3 isn't [negative]

It's an alternating sequence, beginning with the second term, so something probably happened (when n=1) that changed the sign of the first term.

When pondering a pattern for the numerators, think squares. :cool:

 

[wow4201]

Grouping symbol

I found the sequence

[(n^2)-2] / 3^n ................... Grouping symbols added

However I don't know how to handle the alternating part

the sign pattern is,
+,+,-,+,-,+

So neither
(-1)^n

or

(-1)^n-1 or (-1)^n+1 work

 

[mmm4444bot]

I found the sequence

(n^2)-2 / 3^n This is part of it. Good job.

Your grouping symbols (shown in red above) are not correct; they need to enclose the entire numerator. See the last line, in this post.

I don't know how to handle the alternating part Yes you do!

Things are not always as they appear to be.

[This does not work:] (-1)^n

How did you confirm that the following does not work?

(-1)^n * (n^2 - 2) / 3^n

 

[Steven G]

I found the sequence

(n^2)-2 / 3^n

However I don't know how to handle the alternating part

the sign pattern is,
+,+,-,+,-,+

So neither
(-1)^n

or

(-1)^n-1 or (-1)^n+1 work

4bot already stated that this is an alternating sequence starting with the 2nd term.

So your answer is 1/3 + (sigma from 2 to infinity)(-1)^n * (n^2 - 2) / 3^n

 

[mmm4444bot]

...your answer is 1/3 + (sigma from 2 to infinity)(-1)^n * (n^2 - 2) / 3^n

Or, we could say:

Sigma(n = 1 to ∞) [(-1)^n * (n^2 - 2) / 3^n]

This works because n^2 - 2 is negative only when n = 1. :cool: