![\"\"](\"/userfiles/image/steps_images/step1.JPG\")
\ \
\ \
Alternating series test : \ \
\If the alternating series ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=11dda59bda7ee7d803ed2c6c83bdf14d.png\")
satisfies, \ \
(i) ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=7cb67ca545bd52b3a4a3c40fc03493f0.png\")
for all ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=9d9525296c7189f71cd1cbb29d5a4593.png\")
. \ \
(ii) ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=948244a04c2bbf957b3ebb7a9bd6bcdc.png\")
then the series is convergent. \ \
![\"\"](\"/userfiles/image/steps_images/solution.JPG\")
\ \
Alternating series test : \ \
\If the alternating series satisfies, \ \
(i) for all . \ \
(ii) then the series is convergent.