TKChang99

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These are replies submitted by TKChang99

I am truly grateful for time you took to answer my question.

I hope this thread may help others like me.

Now I am going to put together a plan of attack to get at least the basics.

Thank You all again.  This is a great starting point

Studying advanced examples is something I didn't think of, as well as much of your advice.  Thank You,

I hope you don't mind if I print this?

Thanks

@Carl Love 

I learn best by example.  When I didn't quite understand the definition of the command on the help page,  I looked to the examples and tried to parse.  I searched for "Surface" but only a standard mathematical definition came up.  Then I forgot about that part of the description that describes this until you pointed that out.

Thanks again!

Thank You!

I can't believe I missed that!

@Carl Love 

It worked perfectly. I was getting confused, maybe "labels" referred to something else?  I was going bats.  Thanks again!

@TechnicalSupport 

Thanks very much!

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Chapter 8: Infinite Sequences and Series

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Section 8.1: Sequences

 

Essentials

   

NULLExamples

 

 

Example 8.1.1

If a[n] = (2*n^2 - 3*n)/(4*n^3 + 5);, find the limit of the sequence {a[n]}[n = 0]^infinity.

Example 8.1.2

If a[n] = ln(n)/n;, find the limit of the sequence {a[n]}[n = 1]^infinity.

Example 8.1.3

If b[n] = (-2)^(-n)/n;, find the limit of the sequence {b[n]}[n = 1]^infinity.

Example 8.1.4

If a[n] = n!/n^n;, find the limit of the sequence {a[n]}[n = 1]^infinity.

Example 8.1.5

If a[n] = n/(n^2 + 1);, show the sequence {a[n]}[n = 0]^infinity is decreasing.

Example 8.1.6

If a[n] = 5^n/n!;, find the limit of the sequence {a[n]}[n = 0]^infinity.

Example 8.1.7

If a[n]=(1*3*5*⋯*(2 n-1))/(n^(n));, show that the sequence {a[n]}[n = 1]^infinity is decreasing.

Example 8.1.8

If a[1] = 1, a[2] = -1;, and 6*a[n+2]-5*a[n+1]+a[n] = 0 defines a[n] for n > 2, use Maple to find the general term a[n].

Example 8.1.9

a) 

If a[1] = 1; and a[n+1] = 4/(3+2*a[n]) for n > 1,  graph a[n] for n = 1, () .. (), 10.

b) 

Use Maple to find an explicit representation for a[n];.

c) 

Use Maple to calculate limit(a[n], n = infinity);.

Example 8.1.10

If a[n] = (5*n - 4)/(2*n + 3);, determine if the sequence {a[n]}[n = 0]^infinity converges or diverges.

If it converges, find the limit of the sequence.

Example 8.1.11

If a[n] = (n^(1/3) + n^(1/4))/(sqrt(n) + n^(1/5));, determine if the sequence {a[n]}[n = 1]^infinity converges or diverges.

If it converges, find the limit of the sequence.

Example 8.1.12

If a[n] = n!/(n + 2)!;, determine if the sequence {a[n]}[n = 0]^infinity converges or diverges.

If it converges, find the limit of the sequence.

Example 8.1.13

If a[n] = sqrt(n + 5) - sqrt(n);, determine if the sequence {a[n]}[n = 0]^infinity converges or diverges.

If it converges, find the limit of the sequence.

Example 8.1.14

If a[n] = n!/3^n;, determine if the sequence {a[n]}[n = 0]^infinity converges or diverges.

If it converges, find the limit of the sequence.

Example 8.1.15

If a[n] = n^(1/n);, determine if the sequence {a[n]}[n = 1]^infinity converges or diverges.

If it converges, find the limit of the sequence.

Example 8.1.16

If a[n] = (2*n + 5)/sqrt(n^2 + 7*n + 2);, determine the limit of the sequence {a[n]}[n = 0]^infinity.

 

 

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Download uploadcopy.mw

I hope I did this right,  I can't seem to find the file I uploaded anywhere in the preview of this post. Oh! I got it, insert a link. above

@tomleslie 

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