Sue Pemberton Solutions for Chapter: Series, Exercise 13: END-OF-CHAPTER REVIEW EXERCISE 6

Find the term independent of $x$ in the expansion of ${\left(3x^2-\frac{1}{2x^3}\right)}^5$.

Find the first three terms in the expansion of ${\left(x-3x^2\right)}^8$ in descending powers of $x$.

 Find the coefficient of $x^{15}$ in the expansion of $(1-x){\left(x-3x^2\right)}^8$.

Find the first three terms in the expansion of $(1+px{)}^8$ in ascending powers of $x$.

Given that the coefficient of $x^2$ in the expansion of $(1-2x)(1+px{)}^8\text{ is }204$ , find the possible values of $p$.

Find the first three terms in the expansion of $(1+2x{)}^5$ in ascending powers of $x$.

Find the first three terms in the expansion of $(3-x{)}^5$ in ascending powers of $x$.

Find the coefficient of $x^2$ in the expansion of $\left[\right(1+2x\left)\right(3-x){]}^5$