I don't know exactly what resources you can use but for example if an alternating series satisfies the hypothesis of the Leibnitz's rule test then, .
http://math.rutgers.edu/~greenfie/we...fstuff/w4H.pdf
I know for a), I can show it converges with integral test, but how can I find a specific partial sum?
Do I just take the integral from 2 to n of 1/(x*(ln x)^2) and set it <10^-5 so that I get 5 digit accuracy, and then solve for N?
For b), I know how to show divergence, but how do I find the specific partial sum? Same idea?
a) the series...
(1)
... is 'alternate sign' and the absolute value of the genral term decreases monotonically and tends to 0 with n, so that the series converges. For this type of series the truncation error is inferior, in absolute value, to the first 'discharged term' and that happens for...
(2)
Kind regards
Ok thanks, but that part for b) isn't what I had trouble with. Obviously if you take something crazy like 5.5*10^1085, it will work, but how can I find an n for which it will work and the partial sum will exceed 100 using paper and pencil (i.e. no computer programs).