$3\mathrm{.}5$ The infinite series

$f(n)={\displaystyle \underset{i=1}{\overset{n}{}}}\frac{1}{i^4}$

converges on a value of $f(n)=\frac{{}^4}{90}$ as $n$ approaches infinity. Write a program in single precision to calculate $f(n)$ for $n=10,000$ by computing the sum from $i=1$ to $10,000.$ Then repeat the calculation but in reverse order$-$that is$,$ from $i=10,000$ to $1$ using increments of $-1.$ In each case, compute the true percent relative error. Explain the results.