Problem $1$: Consider the harmonic series $S_H={\displaystyle \underset{k=1}{\overset{{10}^N}{}}}\frac{1}{k}.$ Write a MATLAB script program to help you in filling the following table.

$\backslash$table$[[N,\backslash$table$[[S_H$ when using $15$ decimal digits$],[$with number rounding.$]],\backslash$table$[[S_H$ when using $8$ decimal digits$],[$with number rounding.$]]],[5,,],[6,,],[7,,],[8,,]]$