Matching In Exercises 9-14, match the series with the graph of its sequence of partial sums. [The graphs are labeled (a), (b), (c), (d), (e), and (f).] ∑ n = 1 ∞ ( − 1 ) n − 1 4 ( 2 n ) !
Matching In Exercises 9-14, match the series with the graph of its sequence of partial sums. [The graphs are labeled (a), (b), (c), (d), (e), and (f).] ∑ n = 1 ∞ ( − 1 ) n − 1 4 ( 2 n ) !
Matching In Exercises 9-14, match the series with the graph of its sequence of partial sums. [The graphs are labeled (a), (b), (c), (d), (e), and (f).]
Explore the Alternating Series Remainder. (a) Use a graphing utility to find the indicated partial sum Sn and complete the table. (b) Use a graphing utility to graph the first 10 terms of the sequence of partial sums and a horizontal line representing the sum. (c) What pattern exists between the plot of the successive points in part (b) relative to the horizontal line representing the sum of the series? Do the distances between the successive points and the horizontal line increase or decrease? (d) Discuss the relationship between the answers in part (c) and the Alternating Series Remainder
Use a graphing utility to find the indicated partial sum Sn and complete the table, and (b) use a graphing utility to graph the first 10 terms of the sequence of partial sums.
Real Analysis
Prove that the series (a1-a2)+(a2-a3)+(a3-a4)+ . . . converges if and only if the sequence {an}n=1 to infinity converges.
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