Binomial series for any rational power Quiz

1. Find the coefficient of $x^2$ in the expansion of $(1-3x)^{-1}$.

• A. $3$
• B. $9$
• C. $-9$
• D. $6$

2. For which values of $x$ is the expansion of $(3-2x)^{-1}$ valid?

• A. $|x|<\frac23$
• B. $|x|<1$
• C. $|x|<\frac32$
• D. $|x|<3$

3. Find the coefficient of $x^2$ in the expansion of $(1+x)^{\frac12}$.

• A. $-\frac18$
• B. $\frac18$
• C. $\frac14$
• D. $-\frac14$

4. Find the first two terms of the expansion of $(4+x)^{\frac12}$.

• A. $2+\frac x2$
• B. $4+\frac x4$
• C. $2+\frac x8$
• D. $2+\frac x4$

5. Which value of $x$ can be used in the expansion of $(1+2x)^{-3}$?

• A. $x=1$
• B. $x=0.6$
• C. $x=-0.4$
• D. $x=0.5$