How to calculate infinite series?

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Discussion Overview

The discussion revolves around the calculation of the infinite series Ʃ(2^n * x^n), where n starts from 0 to infinity. Participants explore methods to evaluate this series, particularly in relation to geometric series.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty in calculating the series Ʃ(2^n * x^n) and seeks guidance on transforming it into a more manageable form.
  • Another participant suggests letting X = 2x and identifies the series as a classical geometric series Ʃ(X^n).
  • A third participant acknowledges the suggestion and expresses gratitude for the insight.
  • A later reply notes the condition that |X| < 1 must be satisfied to treat the series as a geometric series.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the calculation method, and the discussion includes multiple viewpoints regarding the transformation of the series.

Contextual Notes

The discussion does not clarify the assumptions or conditions under which the series converges, nor does it resolve the mathematical steps involved in the transformation.

thecaptain90
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Hi, I'm stuck on a problem because I don't know how to calculate this series:
Ʃ(2^n * x^n), n starts from 0 to infinity. How can I calculate this? Do I have to transform it into something else where I know the outcome of the Σ like we do with the geometric functions?
 
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thecaptain90 said:
Hi, I'm stuck on a problem because I don't know how to calculate this series:
Ʃ(2^n * x^n), n starts from 0 to infinity. How can I calculate this? Do I have to transform it into something else where I know the outcome of the Σ like we do with the geometric functions?

Let X=2x
Ʃ(X^n) is the classical geometric series.
 
Thanks, didn't think of doing this.
 
Be advised that |X| < 1 to treat this as a geometric series.
 

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