The Chess Problem - Comments and Discussion

The Chess Problem is a silly story that helps students see the difference between arithmetic series and geometric series.

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The Chess Problem - Comments and Discussion

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The Chess Problem - Sequences and Series, published in Directory : Mathematics : Sequences And Series.

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Sequences and Series

fawn75 wrote on Jan 24, 2007

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There seems to be an error in this problem. The story is asking for a cumulative amount on the board. In the first situation, a cumulative amount is shown: $1,000 is added to $2,000 added to $3,000, etc. to total 2,080,000. For the second situation: If a penny is placed in box square, two pennies in the second, four in the third, and so forth... the answer given 1.8 X 10^17 is incorrect. This is only how many pennies there would be in the 64th box ALONE. However, from the story, we are being asked for the total money on the chessboard. The total number would be much greater. Instead, it should be the sum of .01 + .01x2 + .01X2^2 + .01X2^3 + ... .01x2^64.

Maybe the confusion is because the author did not mean to have a cumulative result. The reason I question this is because we are told that the first situation is arithmetic and second is geometric. If I understand correctly, arithmetic would require a linear growth. Geometric is exponential growth. However, in the first situation, according to the answer of 2,080,000, this is NOT an arithmetic sequence. If it was an arithmetic sequence, term 64th should be $64,000 only ($1,000 per box). The answer of $2,080 means the rate of change is NOT constant-- hence not arithmetic. In this case, the second situation answer would be fine in that the 64th term would be .01 X 2^64.

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