Chapter 8: Infinite Sequences and Series
Section 8.2: Series
Use Maple to sum the alternating series ∑n=1∞−1n+1/n2 and show that the sum is the limit of the sequence of partial sums.
Test the claim that a partial sum is closer to the sum than the magnitude of the first neglected term.
Obtain the sum of the series
Control-drag the given series.
Context Panel: Evaluate and Display Inline
∑n=1∞−1n+1n2 = 112⁢π2
Obtain the partial sum Sk and the first few values of Sk
Obtain the first few values of Sk
Obtain the limit of the sequence of partial sums
Calculus palette: Limit operator
Expression palette: Summation template
Sum up through n=k.
limk→∞S__k = 112⁢π2
Maple expresses the partial sum via the special function
Lerch Phi. Nevertheless, Maple's value for Sk will be accepted as correct.
Figure 8.2.3(a) shows the convergence of the first 10 members of the sequence of partial sums to π2/12≐0.82247.
use plots in
Figure 8.2.3(a) Convergence of Sk to S≐0.82247
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