Problem

PART 1: Fill in the blanks.

• Work need not be shown, only answers will be graded.

• 4 points for each blank and 100 points total.

• Each answer need to be clearly labeled on the answer sheet.

• Use of any device with computer algebra system during the exam will result in zero points.

10. Find the sum

• $\displaystyle\sum_{n=2}^{\infty}\frac{(n-2)!+2^n}{n!}=\underline{\quad(13)\quad}$.
• $\displaystyle\sum_{n=1}^{\infty}\frac{1}{2^n-1}\left(\frac{1}{\sqrt{3}}\right)^{2n}=\underline{\quad(14)\quad}$.