Solved: Patterns in coefficients Find the next two terms

Chapter 8, Problem 71E

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QUESTION:

Patterns in coefficients Find the next two terms of the following Taylor series.

\(\frac{1}{\sqrt{1+x}}: \quad 1-\frac{1}{2} x+\frac{1 \cdot 3}{2 \cdot 4} x^{2}-\frac{1 \cdot 3 \cdot 5}{2 \cdot 4 \cdot 6} x^{3}+\cdots\).

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QUESTION:

Patterns in coefficients Find the next two terms of the following Taylor series.

\(\frac{1}{\sqrt{1+x}}: \quad 1-\frac{1}{2} x+\frac{1 \cdot 3}{2 \cdot 4} x^{2}-\frac{1 \cdot 3 \cdot 5}{2 \cdot 4 \cdot 6} x^{3}+\cdots\).

ANSWER:

Solution 71E

Step 1:

Given that

Step2:

To find

Find the next two terms of the following Taylor series.

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