Question

determine whether the series is converges or diverges k=3 sigma k tends to infinity lnk/k

Answer 1

diverges for sure
the denominator is a polynomial of degree 1, so even if the numerator was a constant this would not converge

Answer 2

how...?

Answer 3

if you like you can use the "comparison test" and compare it to \(\sum\frac{1}{k}\)

Answer 4

plz explain now what u sayy...?

Answer 5

hellow comporisn test..?

Answer 6

how can i do comporisn can u explain ..

Answer 7

the denominator in this case is \(k\) and the numerator is \(\ln(k)\) this is larger than the well known divergent harmonic series \(\sum\frac{1}{k}\)
since \(\sum\frac{1}{K}\) diverges, and since \(\frac{\ln(k)}{k}>\frac{1}{k}\) we know \(\sum \frac{\ln(k)}{k}\) diverges as well

Answer 8

why ln(k)/k >1/k