Chapter 8: Infinite Sequences and Series
Section 8.2: Series
Use Maple to sum the series ∑n=3∞4n2−4 and show that the sum is the limit of the sequence of partial sums.
Obtain the sum of the series
Control-drag the series.
Context Panel: Evaluate and Display Inline
∑n=3∞4n2−4 = 2512
Obtain a general expression for the kth partial sum
Control-drag the series and change the upper limit of the sum from ∞ to k.
Context Panel: Assign to a Name≻S[k]
∑n=3k4n2−4 = −1k−1−1k−1k+1−1k+2+2512→assign to a nameSk
Display the first few partial sums
Write Sk and press the Enter key.
Context Panel: Sequence≻k
In the dialog box that appears, set k=3 to k=15
→sequence w.r.t. k
Obtain the limit of the partial sums
Calculus palette: Limit Operator≻Apply to Sk
limk→∞Sk = 2512
Figure 8.2.5(a) shows the convergence of the first 15 members of the sequence of partial sums to S=25/12.
use plots in
Figure 8.2.5(a) Convergence of Sk to S=25/12
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