hello there

i think the key to the proof lies in the fact that:

\(\displaystyle ln(1+p/q)=ln(q+p/q)\)

now this number meaning

\(\displaystyle (q+p)/q\)

is a rational number no matter what p and q are

(as long as they are natural) but it has been proved

that ln(rational number) is always irrational

except for the case where the rational number is 1

but in ur case 1+p/q is always bigger than 1

so u just need to search the proof that ln(rational number)

is always irrational :mrgreen: