Mathematica Warm-Up Problems

Math 242: Modern Computational Mathematics (fall 2024)

Exercise 1: Use a loop with an accumulator to compute partial sums of (1+(1/2)+(1/3)+(1/4)+(1/5)+(1/6)+...). How many terms are required for the sum to exceed 3? How many terms to exceed 4? How many terms to exceed 5?

Exercise 2: Use a loop with an accumulator to compute partial sums of 4(1-(1/3)+(1/5)-(1/7)+(1/9)-(1/11)+...). Experiment by computing sums with more and more terms, following the same pattern. What number results?

Exercise 3: Use a loop with an accumulator to compute
1+(1/(2+(1/(2+(1/(2+(1/2))))))) 
Continue the pattern with more and more nested fractions. The result approaches what number?

Exercise 4: Use a loop with an accumulator to compute
3-(1/(4-(2/(5-(3/(6-(4/(7-...)))))))) 
Continue the pattern with more and more nested fractions. The result approaches what number?