Homework $4$

General instruction: Do the following. Show all the necessary work to get full points. Print this page and sign the attestation below. Write your solutions on clean sheets of paper. If you used more than one sheet, please staple your sheets together. Submit your work on July $28$th$,$ beginning of class.

$(6$ points$)$ Find the radius and the interval of convergence of the series ${\displaystyle \underset{n=1}{\overset{}{}}}(-1{)}^{n+1}\frac{(x+2{)}^n}{n}.$

$(4$ points$)$ Find the exact value of ${\displaystyle \underset{n=0}{\overset{}{}}}\frac{(-3{)}^n}{n!}$ by using a well$-$known Maclaurin series.

$**$ End of homework. $**$

Total points: $10$ points