Does the Series Sum of 1/ln(n+5) from n=1 to Infinity Diverge?

[cloveryeah]

Homework Statement

summation n from 1 to inf, 1/ln(n+5) converge or diverge

Homework Equations

The Attempt at a Solution

1/ln(n+5) > 1/n (from n=2 to inf)

and i proved that it diverges by comparison test, am i correct?
i am thinking that as my prove is n from 2 to inf not from 1 to inf
can i still use this prove?

 

[PeroK]

Homework Statement

summation n from 1 to inf, 1/ln(n+5) converge or diverge

Homework Equations

The Attempt at a Solution

1/ln(n+5) > 1/n (from n=2 to inf)

and i proved that it diverges by comparison test, am i correct?
i am thinking that as my prove is n from 2 to inf not from 1 to inf
can i still use this prove?

What do you think and why?