104lab7solnsF19.pdf - MA104 Lab Report 7 Tests for...

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MA104 Lab Report 7 - Tests for ConvergenceName:Student Number:Fall 20191. [2marks] Supposefis a continuous positive decreasing function forx1 andan=f(n). Rank the following quantities inincreasing order:Z61f(x)dx,5Xi=1ai,6Xi=2aiHint: It may be helpful to draw a picture, considering each quantity in terms of areas.6Xi=2aiZ61f(x)dx5Xi=1ai2. [10marks] Consider the seriesn=1anwherean=e-nn.(a) Use the Integral Test to determine whether the seriesn=1anconverges or diverges. Leave your result as an exact value.[Note: You may assume that the functionf(n) =anis continuous, decreasing, and positive on [1,).]

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