Sequences Assignment.sagews

Sequences Assignment

Question 0

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Question 1

Consider the sequence $\displaystyle a_n=\frac{n^5}{2^n-1}$.

Part a

Graph the first 50 terms of the sequence.

Part b

Estimate the limit of the sequence based on the graph.

Part c

Evaluate the limit using Sage's limit command.

Question 2

Consider the sequence $\displaystyle a_n=\frac{10^n}{n!}$

[Note: Use factorial(n) for $n!$]

Part a

Graph the first 50 terms of the sequence.

Part b

Estimate the limit of the sequence based on the graph.

Part c

Evaluate the limit using Sage's limit command.

Question 3

Consider the sequence $\displaystyle a_n=\frac{n^2}{2n+2}-\frac{n^2}{2n-1}$

Part a

Graph the first 50 terms of the sequence.

Part b

Estimate the limit of the sequence based on the graph.

Part c

Evaluate the limit using Sage's limit command.

Question 4

Consider the sequence defined by $\displaystyle a_1=\sqrt{2}$ and $a_n=\sqrt{2+a_{n-1}}$ for $n\ge2$.

Part a

Graph the first 20 terms of the sequence.

Part b

Estimate the limit of the sequence based on the graph.

Part c

Estimate the limit by computing $a_{50}$.

Question 5

Consider the sequence defined by $\displaystyle a_1=3$ and $a_n=3+\frac{1}{a_{n-1}}$ for $n\ge2$.

Part a

Graph the first 20 terms of the sequence.

Part b

Estimate the limit of the sequence based on the graph.

Part c

Estimate the limit by computing $a_{50}$.

This material was developed by Aaron Tresham at the University of Hawaii at Hilo and is
licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.