Sigma notation for series of numbers

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WilliamsR94

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Feb 5, 2021
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I have the series 243-162+108-72+..., and have to write in sigma notation.

I have worked out the difference to be -2/3 but getting confused with how to write this in notation.
 
WilliamsR94 said:
I have the following series and need to write it out in sigma notation.

243-162+108-72+...,

I have assumed it goes to infinity and the difference is -2/3 but I m really confused and struggling how to write it in sigma notation from my first term
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This is a "Geometric Series" with an initial term (=243) and ratio (= - 2/3). So the series can be written as:

S = 243*(-2/3)0 + (243)*(-2/3)1 + (243)*(-2/3)2 + (243)*(-2/3)3 ........

Now convert it into sigma notation.
 
Thank you, it was the powers that threw me, I didnt think to look at them and ended up dividing the 243 and all sorts

I've got

∞
∑243(-2/3)^n
n=0
 
not the "difference", the common ratio, [MATH]r[/MATH]
[MATH]\sum_{n=0}^\infty a_0 \cdot r^n[/MATH]
 
skeeter said:
not the "difference", the common ratio, [MATH]r[/MATH]
[MATH]\sum_{n=0}^\infty a_0 \cdot r^n[/MATH]
Click to expand...
I was confused by this comment for a second or two, but "difference" refers back to post # 1
 
skeeter said:
the OP double posted ... my response was the first in the duplicate
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Oh I was not trying to correct you. I was briefly puzzled and feared that where I had some trouble seeing the context, a student might have a lot.
 
I understand, just letting you know the two threads were merged.
 
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