Stax, 11 bytes
ó╢Δ'åç4}ú┌7
Explanation:
We want to calculate:
$$\sum_{i=1}^n{\frac 1 i}$$
We now need a denominator \$b\$ and a list of numerators \$a_i\$:
$$\sum_{i=1}^n{\frac{a_i}b}=\frac{\sum_{i=1}^n{a_i}}{b}$$
We can make \$b=n!\$, then we have:
\begin{align} \frac{a_i}{n!}&=\frac 1 i&|\times n! \\ a_i&=\frac{n!}i \end{align}
So we have:
$$\sum_{i=1}^n{\frac 1 n}=\frac{\sum_{i=1}^n{\frac{n!}i}}{n!}$$
|Fx{[/m|+L:_m Full program
|F Factorial
x Push input again
{ m Map over range [1, n]
[ Copy the factorial
/ Divide factorial by current value
|+ Sum
L Listify stack, top gets first element
:_ Divide both values by gcd
m Print each followed by newline
Stax, 11 bytes
ó╢Δ'åç4}ú┌7
Explanation:
We want to calculate:
$$\sum_{i=1}^n{\frac 1 i}$$
We now need a denominator \$b\$ and a list of numerators \$a_i\$:
$$\sum_{i=1}^n{\frac{a_i}b}=\frac{\sum_{i=1}^n{a_i}}{b}$$
We can make \$b=n!\$, then we have:
\begin{align} \frac{a_i}{n!}&=\frac 1 i&|\times n! \\ a_i&=\frac{n!}i \end{align}
So we have:
$$\sum_{i=1}^n{\frac 1 n}=\frac{\sum_{i=1}^n{\frac{n!}i}}{n!}$$
|Fx{[/m|+L:_m Full program
|F Factorial
x Push input again
{ m Map over range [1, n]
[ Copy the factorial
/ Divide factorial by current value
|+ Sum
L Listify stack, top gets first element
:_ Divide both values by gcd
m Print each followed by newline