Patterns in coefficients Find the next two terms of the

Chapter 8, Problem 70E

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QUESTION:

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

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

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QUESTION:

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

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

ANSWER:

Solution 70E

Step 1:

Given that

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