Chapter 8: Infinite Sequences and Series
Section 8.1: Sequences
If an=lnnn, find the limit of the sequence ann=1∞.
If fx=lnxx, then fn=an. Hence, the limit of fx as x→∞ will be the limit of the sequence.
L'Hôpital's rule is a suitable tool for computing limx→∞lnxx=limx→∞1/x1=limx→∞1x=0.
Calculus palette: Limit operator
Context Panel: Evaluate and Display Inline
limn→∞lnnn = 0
Table 8.1.2(a) contains the
task template that, given the general term of a sequence, calculates and graphs its first few members.
First index value
Last index value
plotseq,expr,=.., style=point, symbol=solidcircle, color=red
Table 8.1.2(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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