test for convergence: sigma from n=1 to infinitie of [1-(1/squarerootn)]^n
Follow Math Help Forum on Facebook and Google+
screams comparison test to me. think famous limits. however im pretty rubbish at analysis.
Originally Posted by twilightstr test for convergence: applying the mean value theorem to the function we'll get: now suppose and in put and to get therefore: and hence your series is convergent by the comparison test. (note that and thus the series is convergent by the limit comparison test.)
Originally Posted by NonCommAlg applying the mean value theorem to the function we'll get: now suppose and in put and to get therefore: and hence your series is convergent by the comparison test. (note that and thus the series is convergent by the limit comparison test.)
Originally Posted by NonCommAlg applying the mean value theorem to the function we'll get: now suppose and in put and to get therefore: and hence your series is convergent by the comparison test. Just a quick remark: we can also see this as the usual convexity inequality for , then raised to the power .
View Tag Cloud