Unit 4A Practice Exam B

Analyze the recursive sequence $a_1=1$, $a_{n+1}=\sqrt{3+a_n}$, including its possible limit.

Find the sum of $\sum_{n=2}^\infty 6(1/3)^n$.

Determine convergence of $\sum1/[n(\ln n)^3]$.

Bound the remainder after $N$ terms of $\sum1/n^4$.

Classify $\sum(n^2+1)/(n^4-3)$.

Classify $\sum(-1)^n n/(n+1)$.

Classify $\sum(-1)^n/(n\ln(n+1))$.

Use the Ratio Test on $\sum n^3/2^n$.

Explain why the Root Test is inconclusive for $\sum1/n^7$.

Give a series that converges conditionally and explain both tests.

State and interpret the Cauchy criterion for a series.

Explain why numerical evidence cannot prove convergence.