Identifying correct convergence tests for an infinite series

badatcalc · Oct 11, 2019

To anyone that can help me with this - You have to pick the FIRST correct reason. Work below (exception of 4 because I cannot figure it out), but in order to get the question right you must have all correct and I cannot figure it out. Any help is appreciated.

Multiple-choice question listing reasons A to G why a series diverges, with six series numbered 1 to 6 and answer boxes beside each, filled with letters C, A, C, G, A, F.

Handwritten worked solutions to convergence questions 1 to 3 on lined paper, with p-series and comparison notes for each series.

$Handwritten work on a homework sheet: problem 5 sums (2n+4)/(-1)^n with answer choice (A) divergent as the limit is not zero, and problem 6 sums (-1)^n (2n)!/(n!)^2 with a ratio of |a_{n+1}/a_n| simplified to (2n+2)!/(2n)! times (n!)^2/((n+1)!)^2.$

$Handwritten ratio test working: the limit of |a(n+1)/a(n)| is shown as 4, which is greater than 1, concluding the series diverges by the limit comparison test; the fraction (2n+2)(2n+1)/(n+1)^2 is written above.$

[Moderator's note: Moved from a technical forum and thus no template.]

PeroK · Oct 11, 2019

I'd double check 4 & 6.

Delta2 · Oct 11, 2019

No4 is not that hard once you figure out that ##6^{2n}=(6^2)^n=36^n## and ##(6^2+1)^n=37^n##.

No6 looks fine to me. (oh now I see it says the FIRST reason, might be A afterall).

Identifying correct convergence tests for an infinite series

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