Use the Derivative of the Taylor Series About 0 For \frac{1}{1-x}

question 62

Short Answer

Use the derivative of the Taylor series about 0 for $\frac{1}{1-x}$ to find the Taylor series about 0 for $\frac{x}{(1-x)^{2}}$ .Use this result to find the value of $\frac{1}{4}+\frac{2}{16}+\frac{3}{64}+\frac{4}{256}+\frac{5}{1024}+\cdots$ .Round to 3 decimal places.

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Definitions:

DNA Molecules

Biological structures that carry genetic information vital for cell function, reproduction, and inheritance, composed of two intertwined strands.

Genes

Units of heredity located on chromosomes, made up of DNA, that determine specific characteristics by coding for proteins.

Traits

Characteristics or attributes of an individual, which can be physical, psychological, or behavioral, often considered stable and distinguishing.

Ethnocentrism

The belief in the inherent superiority of one's own ethnic group or culture, often leading to prejudice and discrimination against others.