Mathematics 150BL

Inclass Assignment 2.

We continue to learn Scientific Notebook. Today let's look at sequences.

Recall that a sequence can be thought of as a list of numbers written in a definite order

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Notice that for every positive integer $n$ there is a corresponding number $a_{n}$ and so a sequence can be defined as a function whose domain is the

set of positive integers. (However, we usually write $a_{n}$ instead of $f(n).$)

Example:

1. Consider MATH
m150b1pt2__7.png

Pull down on the "compute" menu and hit the "new definition."

You are asked if you want a function argument or part of the name.

Pick "function argument." You can now evaluate

$\vspace{1pt}$

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Let's plot the sequence. To do this choose Plot 2D+Rectangular. Then open the Plot Properties dialogue box (the little blue box in the corner) choose Items Plotted , Plot Style "Points" , and Point Marker "Box". In the above plot we used the Plot Interval 11 $\leq n\leq $ 50; and 40 sample points. It is important that the number of sample points is identical to the number of positive integers in the Plot Interval. Look at the graph. Does the sequence approach a limit?

Guess....

2 : We can compute the limit by evaluating

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Part II of Assignment 1 - due 2/7

Exercises: In the following problems, plot the given sequences, evaluate them for n = 1; 10; 100; 1000 and compute the limit:

i . $c_{n}=n^{2}/2^{n}$

ii. MATH

iii. $e_{n}=$ MATH

iv. MATH

This document created by Scientific Notebook 4.0.