sum of this infinite series

the series diverges by p-test .
As each terms are positive & the series diverges ,
the sum = + infinity

2012-01-28 13:42:38 補充：
p-test :
For p > 1 , the series sum(i from 1 to inf.)[ (1/i)^p ] converges
For p <= 1 , the series sum(i from 1 to inf.)[ (1/i)^p ] diverges

it is the corollary of integral test ( consider f(x) = 1/x^p )
'http://en.wikipedia.org/wiki/Integral_test_for_convergence'

_1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+...>1+1/2+1/4+1/4+1/8+1/8+1/8+1/8+...=1+1/2+1/2+1/2+...=∞ So, 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+...=∞.