# Chapter 8, Sequences and Series - Section 8.6 - The Binomial Theorem - 8.6 Exercises - Page 636: 16

$(2+ \frac{x}{2})^{5}=32+40x+20x^{2}+5x^{3}+\frac{5}{8}x^{4}+\frac{1}{32}x^{5}$

#### Work Step by Step

We use the values from the 5th row of Pascal's Triangle to find the coefficients: $(2+ \frac{x}{2})^{5}=(2)^{5}+5(2)^{4}(\frac{x}{2})^1+10(2)^{3}(\frac{x}{2})^{2}+10(2)^{2}(\frac{x}{2})^{3}+5(2)^1(\frac{x}{2})^{4}+(\frac{x}{2})^{5}=32+40x+20x^{2}+5x^{3}+\frac{5}{8}x^{4}+\frac{1}{32}x^{5}$

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