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).]
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Chapter 9 Solutions
Calculus
- How is finding the sum of an infinite geometric series different from finding the nth partial sum?arrow_forwardFinding a Sum In Exercises 55-60, find the partial sum. n=150narrow_forwardProving the Alternating Series Test (Theorem 2.7.7) amountsto showing that the sequence of partial sums sn = a1 − a2 + a3 −· · ·±an converges. (The opening example in Section 2.1 includes a typical illustration of (sn).) Different characterizations of completeness lead to different proofs. (a) Prove the Alternating Series Test by showing that (sn) is a Cauchysequence. (b) Supply another proof for this result using the Nested Interval Property(Theorem 1.4.1). (c) Consider the subsequences (s2n) and (s2n+1), and show how the Monotone Convergence Theorem leads to a third proof for the Alternating Series Test.arrow_forward
- Odd and Even Digits in Pi A New York Times article about the calculation of decimal places of π noted that “mathematicians are pretty sure that the digits of π are indistinguishable from any random sequence.” Given below are the first 25 decimal places of π. Test for randomness in the way that odd (O) and even (E) digits occur in the sequence. Based on the result, does the statement from the New York Times appear to be accurate?arrow_forwardevaluation of its sum using two consecutive partial sums (if the alternating series is convergent (conditionally orabsolutely), then compute, otherwise just present and explain the formula for evaluating).arrow_forwardCalc and Anal Geometry II SHOW ALL WORK Use the Ratio test to determine whether the series converges or diverge ∞ ∑ (-1)n(2n+1)/n! n=1arrow_forward
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning