Question

how would I find the sum for other telescoping series for the series ( ln 1/2 + ln 2/3 + ln 3/4 )

Answer 1

you could make use of the rule:
In(a) + In(b) = ln(ab)

Answer 2

you should then notice the denominator and numerators of the fractions cancelling each other out

Answer 3

ln 1/2 + ln 2/3 + ln 3/4 + ...
ln 1 - ln 2 + ln 2 -ln 3 + ln 3 - ln 4+ ......

Answer 4

If you take it as an infinite series, then it diverges to -Infinity