We will now show that two different rearrangements of the alternating harmonic series add up to two different values.
(1) Consider[infinity]∑k=1(−1)k+1k= 1−12+13−14+15−16+17−···In the PreLab you showed that this series converged by satisfying the hypotheses of the Alternating Series Test. Thus, we may use the Remainder in Alternating Series (Theorem 8.20 in the text) Theorem to bound the actual sumS.

(a) Note that the first partial sum, S1= 1.
(i) The Remainder in Alternating Series Theorem states that the actual sumS(of which we will not determinethe exact value here) satisfies|S−S1|<.
(ii) Using properties of absolute values< S−S1<
(iii) AddingS1= 11−< S <1 +(iv) We concludeS <

(b) We repeat the steps forS2=
(i) the actual sumSsatisfies|S−S2|<.
(ii) Using properties of absolute values< S−S2<
(iii) So,< S <(iv) We concludeS

A25- foot ladder leans against a building and reaches a point of 23.5 feet above the ground .find the angle that the ladder makes with the building

Acompany charges $0.10 for each letter engraved. bobby plans to spend no more than $5.00 on the engraving on a jewelry box. write and solve an inequality to find the maximum number of letters he can have engraved.

Name and describe the three most important measures of central tendency. choose the correct answer below. a. the mean, sample size, and mode are the most important measures of central tendency. the mean of a data set is the sum of the observations divided by the middle value in its ordered list. the sample size of a data set is the number of observations. the mode of a data set is its highest value in its ordered list. b. the sample size, median, and mode are the most important measures of central tendency. the sample size of a data set is the difference between the highest value and lowest value in its ordered list. the median of a data set is its most frequently occurring value. the mode of a data set is sum of the observations divided by the number of observations. c. the mean, median, and mode are the most important measures of central tendency. the mean of a data set is the product of the observations divided by the number of observations. the median of a data set is the lowest value in its ordered list. the mode of a data set is its least frequently occurring value. d. the mean, median, and mode are the most important measures of central tendency. the mean of a data set is its arithmetic average. the median of a data set is the middle value in its ordered list. the mode of a data set is its most frequently occurring value.