Intro Mathematica Assignment

Math 242 Modern Computational Math, spring 2021

Complete the following exercises before class on Wednesday, February 17. You can do the work in this notebook, below each numbered item. Upload your solutions as a Mathematica notebook to the Intro Mathematica assignment on the Moodle site for Math 242.

Use a loop with an accumulator to compute partial sums of the following:

s=1+(1/4)+(1/9)+(1/16)+(1/25)+…

Then take your sum s and compute (Sqrt[6s]). Experiment by doing this for sums with more and more terms, converting your results to decimal numbers. To what number do your results appear to converge?

Use a loop with an accumulator to compute partial products of the following:

r=2((4/3))((16/15))((36/35))((64/63))…

Experiment by computing products with more and more factors, following the same pattern. To what number do your results appear to converge?

Compute the following expression:

q=1+(1/(1+(1/(1+(1/(1+(1/(1+...))))))))

Experiment by computing more and more nested fractions, following the pattern above. To what number do your results appear to converge?

Hint: Start from the bottom!