Chapter 3, Problem 5P

The infinite series

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

converges on a value of $f\left(n\right)={\pi }^4/90$ as n approaches infinity. Write a program in single precision to calculate $f\left(n\right)\text{ for }n=10,000$ 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.