Question

log( 1/2)+log(2/3)+...............+log(99/100)=

Answer 1

we know loga + logb= log(ab)

so for this expanson we can write it as

log(1/2 * 2/3 * 3/4 * 4/5 * .............98/99 * 99/100)

here we can see many terms will cancel each other only remaining with

log(1/100)

= -log(100)

= -2