What is the sum from n=5 to infinity of ln(n)-ln(2n) ?

The sum from n=5 to infinity of ln(n)-ln(2n) is diverges

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sum from n=5 to infinity of ln(n)-ln(2n)

n = 5 \sum \infty ln (n) - ln (2 n)

diverges

Solution steps

n = 5 \sum \infty ln (n) - ln (2 n)

ln (n) - ln (2 n) = - ln (2)

= n = 5 \sum \infty - ln (2)

Every infinite sum of a non-zero constant diverges

= diverges

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What is the sum from n=5 to infinity of ln(n)-ln(2n) ?
The sum from n=5 to infinity of ln(n)-ln(2n) is diverges