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Consider the series ((-1)^(n+1))/(n^(61/62)) ( lower bound n = 1; upper bound = inf) which converges conditionally.

(a)

Define a function that generates the terms of the series, and a function that generates the

partial sums; define the partial sums as decimal approximations to 8 significant digits.

Then make a DiscretePlot of the partial sums for k from 1 to 50, with Filling None

Approximately what does the series converge to?

(b)

Define functions for the following scrambled sums.

Alternating 2 positive terms, 1 negative term, 2 positive, 1 negative, etc.

Alternating 1 positive term, 2 negative, 1 positive, 2 negative, etc.

Alternating 4 positive terms, 1 negative term, 4 positive, 1 negative, etc.

Alternating 2 positive terms, 11 negative terms, 2 positive, 11 negative, etc.

Use DiscretePlot to plot all five partial sum functions together (including the

original un-rearranged partial sums), for k from 1 to 50, with Filling None

Make a table that shows k together with all five partial sum functions (including

the original un-rearranged sums), for k from 1 to 50, and display as a Grid. (The

sums should all be displayed as decimal numbers.)

Do the rearranged partial sums converge to the same limit as the original un-scrambled series?

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