Lemma

Calculus · Chapter 15 of 16

Series

5 curated · 119 from open sources · 9,200 generated

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From open sources

119

Complete problems only, with worked solutions first. Show everything

#TitleDifficulty
134473Estimate … by comparison with an integralMedium
134474If … converges (all …) show that … convergesMedium
134475If … converges (all …) show that … convergesMedium
134476Construct a series … that converges faster than … but slower than…Medium
134481For the series … show that the ratio test failsDeep
134482Decide convergence in 57–66 and name your testDeep
134486Deep
134490… (test all …)Deep
134492… (test all …)Deep
134496Easy
134498Easy
134500Easy
134502Easy
134504Easy
134506Easy
134509Show that the alternating series … does not converge, by computing the…Easy
134514Give a bound on the difference between … andMedium
134516Does the alternating series in 20 or the positive series in 21…Medium
134518Find conditions which guarantee that … will converge (negative term follows two…Medium
134519If the terms of … are rearranged into …, show that this…Medium
134520Show that the series … converges toMedium
134521What is the sum ofMedium
134522Combine … and … to proveMedium
134523(b) Show that its sum is Euler's constantMedium
134524Prove that this series convergesMedium
134526The sine of … radians isMedium
134528Verify the Schwarz inequality … if … andMedium
134530For a conditionally convergent series, explain how the terms could be rearranged…Deep
134531Describe the terms in the product … and find their sumDeep
134532True or false: (a) Every alternating series convergesDeep
134533Every number … between 0 and 2 equals … with suitable terms…Deep
134535Show that no choice of signs will make … equal to zeroDeep
134537Suppose … converges andDeep
134384The geometric series isEasy
134394Show that … is not a fractionEasy
134396Write … and … as fractions and as geometric seriesEasy
134398Easy
134400Easy
134402Easy
134404Medium
134406Medium
134418Compute the …th derivative of … atMedium
134424Compute … to its second decimal place without a calculator (OK to…Deep
134426Two tennis players move to the net as they volley the ballDeep
134433Easy
134437Easy
134439Easy
134447Easy
134449Easy
134451Easy
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