Question

Use the properties of logarithms to simplify the partial sums of the series log( k/k+1 ) Decide if the series is convergent or divergent .

Answer 1

log k/(k+1) = log k - log(k+1)

so, summing 1..n, that's
log1 - 2log2 + log2 - log3 + ... + log(n-1) - log n = 0 - log n