Solving the B Sequence: Tips and Tricks for Finding the Closed-Form Solution

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Discussion Overview

The discussion revolves around finding a closed-form solution for the sequence B = 1, -1/2, +1/4, -1/8, +1/16, ... Participants are exploring various representations and formulations of the sequence, focusing on the mathematical expressions that could describe it effectively.

Discussion Character

  • Exploratory, Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty in solving the sequence and seeks assistance in finding a closed-form representation.
  • Another participant suggests the expression (-1/2)^n, indicating that n starts from 0.
  • A different participant proposes the expression 1/(-2)^n, questioning its validity and noting that it appears similar to the previous suggestion.
  • There is a clarification regarding the inclusion of 0 in the number line and a mathematical property that (a/b)^n = a^n/b^n.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the closed-form solution, as multiple expressions have been proposed without agreement on which is correct.

Contextual Notes

There are unresolved aspects regarding the representation of the sequence, particularly concerning the initial term and the implications of including 0 in the number line.

mknabster
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This sequence is stumping me, how would I go about solving this?

Write the sequence B = 1, -1/2, +1/4, -1/8, +1/16, ... in closed-form. I tried using (-1) has the top with different variable son the bottom, but nothing seems to add up. The 1 in the front is throwing me off. Any help would be appreciated. thank you
 
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(-1/2)n, where n starts from 0.
 
Oh so you do include 0 in the number line. HOw does this look: 1/(-2)n
 
mknabster said:
Oh so you do include 0 in the number line. HOw does this look: 1/(-2)n
It looks the same. -1/2 = 1/(-2)

Also (a/b)n = an/bn
 

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