does the series: summation from 1 to infinity (-1)^n (n^2) / [n^2 + n] converge? why cant i say that since (n^2) / [n^2 + n] is decreasing and greater than 0, by alternating series test, it converges? the ans says that it diverges.
Follow Math Help Forum on Facebook and Google+
Originally Posted by alexandrabel90 does the series: summation from 1 to infinity (-1)^n (n^2) / [n^2 + n] converge? why cant i say that since (n^2) / [n^2 + n] is decreasing and greater than 0, by alternating series test, it converges? the ans says that it diverges. Note that This limit does not go to zero (it does not exist) so the series diverges by the basic divergence test.
Originally Posted by alexandrabel90 does the series: summation from 1 to infinity (-1)^n (n^2) / [n^2 + n] converge? why cant i say that since (n^2) / [n^2 + n] is decreasing and greater than 0, by alternating series test, it converges? the ans says that it diverges. Does ? Sometimes it is highly advisable to think a little about a problem BEFORE rushing up to ask for help... Tonio
View Tag Cloud