Question $3.$ Consider a sequence $\{b_n{\}}_n=1^{}.$ We say that the infinite product ${}_n=1^{}{b}_n$ converges to pin$\frac{R}{\frac{?}{?}}\{0\}$ if $\underset{n}{lim}{}_k=1^n{b}_k=p.$

If the product does not converge to any pin$\frac{R}{\frac{?}{?}}\{0\},$ we say it diverges.

a$)$ Prove that if ${}_n=1^{}{b}_n$ converges, $\underset{n}{lim}{b}_n=1.$

b$)$ Find ${}_n=1^{}\frac{n^3+n^2+n}{n^3+1}$ or show that the product diverges.