Consider the Series $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } \frac { 1 } { 2 n - 1 }$

question 80

Essay

Consider the series $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } \frac { 1 } { 2 n - 1 }$ .(a) Show that the series is convergent, but not absolutely convergent.(b) Calculate the sum of the first 9 terms to approximate the sum of the series.(c) Is the approximation in part (b) an overestimate or an underestimate?
(d) Estimate the error involved in the approximation from part (b).

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Definitions:

Steroid Hormones

Lipid-soluble molecules derived from cholesterol that regulate a variety of physiological functions including metabolism, inflammation, and sexual function.

Plasma Membrane

The lipid bilayer that surrounds a cell, controlling the passage of substances in and out of the cell.

Phosphodiesterase

Enzyme that splits phosphodiester bonds—that is, that breaks down cyclic AMP to AMP.

Phosphodiesterase

An enzyme that plays a role in cell signal transduction by breaking down phosphodiester bonds.