Chapter 12.5 Puzzle

This assignment is due 48 hours after the Chapter Test is given.

• Puzzle solutions are due by 5:00 PM two days after the Chapter Test.
• Puzzles are worth 10 points of extra credit each.
• Answers must be accompanied by valid reasoning. Just like the tests, the answer alone isn't enough!
• Please enter your solution in the text area at the bottom of this page. DON'T FORGET TO GIVE YOUR NAME!

Compute the first six partial sums of . This series is called the alternating harmonic series.

Will any of the partial sums of the alternating harmonic series exceed 1? Will any of the partial sums of the alternating series be negative? Explain your answers.

Fill in the first 14 terms of the alternating harmonic series in the top row of boxes provided below. Be sure to put the + and ­ signs inside the boxes.

Fill in the first seven terms of half the alternating harmonic series in the middle row of boxes. (Note that each box in the second line is not equal to half of the box directly above it, due to the way we staggered the boxes).

Add the series for X to the series for X/2 to get a series for 3X/2. Do this by adding column by column.

Note that the terms in the series 3X/2 are exactly the same as the terms for the series for X. That is, the series for 3X/2 is a rearrangement of the series for X. Can we conclude that the sum 3X/2 is the same as the sum X? That is, does it follow that 3X/2 = X?

Don't forget to explain your answer as clearly as possible.

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