▁responsible ▁for ▁the ▁more ▁powerful ▁ 1 8 6 8 ▁Hawai i ▁earth qu ake ▁and ▁t sun ami . ▁ ▁See ▁also ▁List ▁of ▁earth qu akes ▁in ▁ 1 9 7 5 ▁List ▁of ▁earth qu akes ▁in ▁Hawai i ▁List ▁of ▁earth qu akes ▁in ▁the ▁United ▁States ▁ ▁References ▁ ▁External ▁links ▁US GS ▁Hawai ian ▁Vol cano ▁Observ atory ▁T sun ami ▁An imation : ▁Hawai i ▁ 1 9 7 5 ▁– ▁Pacific ▁T sun ami ▁Warning ▁Center ▁ ▁Category : 1 9 7 5 ▁earth qu akes ▁Category : E arth qu akes ▁in ▁Hawai i ▁Category : Ge ography ▁of ▁Hawai i ▁( is land ) ▁Category : 1 9 7 5 ▁t sun am is ▁Hawai i ▁earth qu ake <0x0A> </s> ▁In ▁mathematics , ▁Dir ich let ' s ▁test ▁is ▁a ▁method ▁of ▁testing ▁for ▁the ▁convergence ▁of ▁a ▁series . ▁It ▁is ▁named ▁after ▁its ▁author ▁Peter ▁Gustav ▁Le je une ▁Dir ich let , ▁and ▁was ▁published ▁post hum ously ▁in ▁the ▁Journal ▁de ▁Math ém atiques ▁P ures ▁et ▁App liqu ées ▁in ▁ 1 8 6 2 . ▁ ▁Stat ement ▁▁ ▁The ▁test ▁states ▁that ▁if ▁ ▁is ▁a ▁sequence ▁of ▁real ▁numbers ▁and ▁ ▁a ▁sequence ▁of ▁complex ▁numbers ▁satisfying ▁▁▁ ▁is ▁monot onic ▁▁▁▁▁▁ ▁for ▁every ▁positive ▁integer ▁N ▁ ▁where ▁M ▁is ▁some ▁constant , ▁then ▁the ▁series ▁ ▁converges . ▁ ▁Proof ▁▁ ▁Let ▁ ▁and ▁. ▁ ▁From ▁summ ation ▁by ▁parts