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2.4 Sum of Integers
Note: This exercise serves as an introduction to 2.5 The Partition Function.
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Question 1 of 4
1. Question
Consider an integer, say 5. Notice how many ways can 5 be broken into the sum of integers.
1+1+1+1+1, 1+2+1+1, 1+2+2, 2+3, 1+3+1, 1+4, and 5, which means 7 ways.
How many ways can 6 be broken into the sum of integers?
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Question 2 of 4
2. Question
How many ways can 8 be broken into the sum of integers?
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Question 3 of 4
3. Question
Now that you understand the concept of breaking up integers into sums of integers, let’s develop an easier way to calculate the number of sums using a formula.
Which formula predicts the number of sums up to 6 with the greatest precision?
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Question 4 of 4
4. Question
In the last question, the formula f(x) = 2x - 2 gave us pretty good results up to the integer 6. Now test the predictive power of the formula we discovered and see how well it works with bigger integers. Which formula predicts the number of sums up to 10 with the best precision?
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