About general harmonic series

By comparsion with the divergent series Σ(n = 0 to ∞) 1/n
lim (n-> ∞) an/bn=lim(n->∞) (1/an+b)/(1/n)=n/(an+b)=1/a>0
From the limit comparsion test, Σ(n = 0 to ∞) [1/(an + b)] , where a and b are any real numbers and none of the term of an + b is 0 , is always divergent

Since none of an + b is zero, b is non-zero since if b = 0, an + b = 0 when n = 0
So by case consideration:
Case 1: a,b > 0
http://i117.photobucket.com/albums/o61/billy_hywung/Jan09/Crazyseries7.jpg
And for a,b < 0, similar approach.

2009-01-30 15:50:31 補充：
Case 2: a > 0, b < 0
http://i117.photobucket.com/albums/o61/billy_hywung/Jan09/Crazyseries8.jpg
http://i117.photobucket.com/albums/o61/billy_hywung/Jan09/Crazyseries9.jpg
And for a < 0, b > 0, similar approach

2009-01-30 15:51:36 補充：
Case 3: a = 0
Result is obvious since all terms are of equal non-zero value.