Chapter 8: Infinite Sequences and Series
Section 8.1: Sequences
Example 8.1.6
If an=5nn!, find the limit of the sequence ann=0∞.
Solution
Mathematical Solution
Note that an>0 for all n≥0, and write the general term in the sequence as
an=5⋅5⋅5⋅5⋅51⋅2⋅3⋅4⋅5⋅56⋅57⋅58⋅⋯⋅5n<544!⋅55⋅55⋅⋯⋅55⋅5n=554!⋅1n
from which it follows by a discrete form of the Squeeze theorem that limn→∞an=0.
Maple Solution
Calculus palette: Limit operator
Context Panel: Evaluate and Display Inline
limn→∞5nn! = 0
Table 8.1.6(a) contains the task template that, given the general term of a sequence, calculates and graphs its first few members.
Tools≻Tasks≻Browse: Algebra≻Sequences
Sequences
General term
expr≔5nn!
expr:=5nn!
Index name
n
First index value
0
Last index value
12
Members
seqexpr,=..
1,5,252,1256,62524,62524,3125144,156251008,781258064,39062572576,390625145152,19531251596672,976562519160064
Graph
plotseq,expr,=.., style=point, symbol=solidcircle, color=red
Table 8.1.6(a) The Sequences task template
Place the cursor somewhere in the cell containing the phrase "General term"and press the Tab key often enough for the cursor to move to, and select the default general term. With this expression auto-selected, simply overwrite with the desired general term, most easily obtained by a copy/paste operation. Then, adjust any of the inputs as needed, and simply press the Enter key to execute each command in the template.
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