Determine whether the given series is absolutely convergent, conditionally convergent, or divergent. Support your conclusion with a well-written argument that names any series test used, shows the conditions of the series test(s) utilized are met, provides calculation(s) to show a conclusion can be made, and summarizes your findings at the end. (a) In=1(-1)"sin () (-1)" (n-2) (C) 2n=1 ºnin (c) En=1 (e) En=4 (-1)", (b) 20 (-1)" (n2+n+ 2) (0) 2n=1 n42) (d) =2 (–1)M (1+2)" (1) =1 (–1)n+1 2012 4+ 2n+ 3 4) Consider the series En a) Show the series is convergent and determine the type of convergence. Be sure to provide a careful argument to prove the type of convergence and name any series tests you apply. b) What is the smallest integer N so that SN approximates the sum of the series accurate to less than 10-4? What is this approximation? c) Is the approximation given in part (b) an overestimate or an underestimate? Explain.

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Step-by-step explanation:

in summarizing the findings at the end. with (a) In=1(-1)"sin () (-1)" (n-2) (C) 2n=1 ºnin (c) En=1 (e) En=4 (-1)", (b) 20 (-1)" (n2+n+ 2) (0) 2n=1 n42) (d) =2 (–1)M (1+2)" (1) =1 (–1)n+1 2012 4+ 2n+ 3 4) Consider the series En

As well as to calculate the smallest integer, The negative integers will go on with no bound and getting lesser and lesser for ever.

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d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

cant open file sorry!

step-by-step explanation: