Alexb:
The question is not a homework. I do it for my own intrest.
You think that the question is in the syllabus of S-4?
With a calculator and subsituting big values, it can be shown that the series diverges.I knew this before I post the question. But how can I do it with mathematical means?
I tried hard to find the limit of the general term, but the term is ¡u¡Û/¡Û¡v,so I diffentiate it. But logarithmetic diffrentiation keeps on giving back exponential invloves nth or composition of nth power.So ratio tests and the n-th term test for divergence is of no use.
I have think of comparison with e, because after some algebaric operations, the term is something like (1+(something)/(f(n)))^n ,like e very much. But I can't do further to make the term be something related with e.
I've done anything I can do,including ask anyone who may know how to do it.So, can you help me?
Finian