Partial sum of geometric series

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Discussion Overview

The discussion revolves around calculating the partial sum of a geometric series, specifically focusing on how to derive the sum of every other term in the series. Participants explore methods for summing terms at odd and even indices within the series.

Discussion Character

  • Exploratory, Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant expresses knowledge of calculating the partial sum of a geometric series but seeks a method to sum only every other term.
  • Another participant suggests rewriting the series as another geometric series, indicating that for an odd number n, it can be expressed as n=2m+1, where m is an integer.
  • A different participant mentions needing to calculate the sum for even-indexed terms and implies they have found a solution without detailing it.
  • It is noted that for even n, represented as n=2m, the sum can be expressed as (.25)m, indicating it is also a geometric series.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the specific equations to use for summing every other term, and multiple approaches are discussed without resolution.

Contextual Notes

Participants' discussions depend on the definitions of odd and even indices and the structure of the geometric series. Some assumptions about the values of n and m are present but not fully articulated.

realitybugll
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ok so i know how to calculate the partial sum of a geometric series.

But let's say i only want to calculate the sum of every other term, how would i do this?

example:

.5^0+.5^1+.5^2+...+.5^n = (.5^(n+1) - 1)/(.5-1)

but what equation can i use to get the sum of only these terms:

.5^1+.5^3+.5^5...+.5^n where n is odd
 
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Hint:

See if you can re-write it as another geometric series, utilizing that an odd number n=2m+1, for m integer.
 
yea i actually need to do it for the even ones for my equation haha

ok so i think i got it, not going to write it all out because i;m busy, but thank you :)
 
And, of course, (.5)n, for n, even, n= 2m, is (.25)m so you have just another geometric series.
 

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