Chapter 11, Problem 6CRQ

a.

To determine

To fill: The blank in the statement “If ${\displaystyle \sum _{n=1}^{\infty }{a}_n}$ converges, then $\underset{n\to \infty }{\lim }{a}_n=\_\_\_\_\_$. If $\underset{n\to \infty }{\lim }{a}_n$ does not exist or if $\underset{n\to \infty }{\lim }{a}_n\ne 0$, the ${\displaystyle \sum _{n=1}^{\infty }{a}_n}\_\_\_\_$”.

b.

To determine

To fill: The blank in the statement “If ${\displaystyle \sum _{n=1}^{\infty }{a}_n}=A$ and ${\displaystyle \sum _{n=1}^{\infty }{b}_n}=B$ and c is any real number, then ${\displaystyle \sum _{n=1}^{\infty }\left(c{a}_n+bn\right)}=\_\_\_\_\_$”.