Chapter 8: Infinite Sequences and Series
Section 8.2: Series
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Example 8.2.5
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Use Maple to sum the series and show that the sum is the limit of the sequence of partial sums.
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Solution
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Obtain the sum of the series
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Control-drag the series.
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Context Panel: Evaluate and Display Inline
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Obtain a general expression for the th partial sum
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Control-drag the series and change the upper limit of the sum from ∞ to .
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Context Panel: Evaluate and Display Inline
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Context Panel: Assign to a Name≻S[k]
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Display the first few partial sums
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Write and press the Enter key.
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Context Panel: Sequence≻
In the dialog box that appears, set to
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Obtain the limit of the partial sums
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Calculus palette: Limit Operator≻Apply to
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Context Panel: Evaluate and Display Inline
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Figure 8.2.5(a) shows the convergence of the first 15 members of the sequence of partial sums to .
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use plots in
module()
local SK,X,Y,p1,p2,p3,k;
unassign('S');
SK:=k->sum(4/(n^2-4),n=3..k);
X:=[seq(k,k=3..15)];
Y:=[seq(SK(k),k=3..15)];
p1:=pointplot(X,Y,symbol=solidcircle,symbolsize=15,color=red,labels=[k,typeset(S[k])],view=[0..15,0..2.5]);
p2:=plot(25/12,k=0..15,color=black);
p3:=display(p1,p2);
print(p3)
end module:
end use:
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Figure 8.2.5(a) Convergence of to
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