Postby Technomancer » Tue Apr 18, 2006 9:00 pm
This sequence does not converge. Your answer could have been checked in a relatively straightforward manner: Notice that in the limit, the argument of the natural logarithm becomes ~0.5. In other words, if you ignore the first few terms, you are repeatedly summing a non-zero constant (ln 0.5), which will inevitably go to infinity. This means that the series fails the Divergence test since the limit of the individual terms must be equal to zero.
The scientific method," Thomas Henry Huxley once wrote, "is nothing but the normal working of the human mind." That is to say, when the mind is working; that is to say further, when it is engaged in corrrecting its mistakes. Taking this point of view, we may conclude that science is not physics, biology, or chemistry—is not even a "subject"—but a moral imperative drawn from a larger narrative whose purpose is to give perspective, balance, and humility to learning.
Neil Postman
(The End of Education)
Anti-intellectualism has been a constant thread winding its way through our political and cultural life, nurtured by the false notion that democracy means that my ignorance is just as good as your knowledge
Isaac Aasimov
