$(3$pts ea$)$ Matching: There is an extra one!

$e^x$

$sinx$

$cosx$

$\frac{1}{1-x}$

$5$

$6.$ convergent p$-$series

$7.$ divergent p$-$series

A$.{\displaystyle \underset{n=0}{\overset{}{}}}\frac{3}{2^n}$

B$.{\displaystyle \underset{n=0}{\overset{}{}}}(-1{)}^n\frac{x^{2n}}{(2n)!}$

C$.{\displaystyle \underset{n=0}{\overset{}{}}}\frac{x^n}{n!}$

D$.{\displaystyle \underset{n=0}{\overset{}{}}}\frac{1}{n^5}$

H$.{\displaystyle \underset{n=0}{\overset{}{}}}(\frac{k}{n})x^{k-n}$

E$.{\displaystyle \underset{n=0}{\overset{}{}}}\frac{1}{\sqrt[\phantom{2}]{n}}$

F$.{\displaystyle \underset{n=0}{\overset{}{}}}(-1{)}^n\frac{x^{2n+1}}{(2n+1)!}$

G$.{\displaystyle \underset{n=0}{\overset{}{}}}{x}^n$