Rearranging Series to Equal SQRT2: How to Solve

Thread starter andrey21
Start date Nov 30, 2010
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Series

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SUMMARY

The discussion focuses on rearranging the series defined by the formula ((-1)^(n-1))/(n) to equal SQRT(2). Participants suggest a systematic approach of alternating between positive and negative terms to achieve the desired sum. Additionally, they explore various series, including 1/4 + 1/10 + 1/18 + 1/28 + ..., and derive a general term for this sequence. The limit of the series is determined to be 11/18, and the convergence of other series is discussed, including geometric series and their sums.

PREREQUISITES

Understanding of series and convergence concepts
Familiarity with partial fractions and telescoping series
Knowledge of limits and algebraic manipulation
Basic understanding of geometric series and their sums

NEXT STEPS

Study the convergence criteria for series, particularly geometric series
Learn about telescoping series and how to derive their limits
Explore the binomial theorem and its applications in limits
Investigate the properties of alternating series and their convergence

USEFUL FOR

Mathematicians, students studying calculus or series convergence, and anyone interested in advanced algebraic techniques for solving series problems.

Dec 1, 2010

micromass

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Yes, I suppose so...

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Dec 1, 2010

andrey21

Great Thank u micromass now I just need to work out the binomia therom part of the question.

Dec 6, 2010

andrey21

Hey micromass could u possibly help me on a thread I've created regarding a partial differential equation. I am having a little trouble. Thanks in advance.