The infinite series $($the $$Basel problem$)$

$()=,1$

$$ $

$*$

$+,($

converges to a value of $()=$ $ $/6$ as $$ approaches infinity.

a$)$ Write a program in single precision to calculate $()$ for $=10,000$ by computing the sum from

$=1$ to $10,000.$ Compute the true percent relative error.

b$)$ Repeat the calculation from a$)$ but in reverse order $($that is$,$ from $=10,000$ to $1)$ using increments

of $-1.$ Again, compute the true percent relative error.

c$)$ Explain the results, thinking about how numbers are represented on a computer