![\"\"](\"http://www.mathskey.com/userfiles/image/steps_images/step1.JPG\")
The time elapsed is ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=b2ba2fd5c82215355ebea094bb84b70c.png\")
.
Find the total time.
\A geometric series with ratio ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=cc9bb0729dc9c8bf32a7cdd2a48bca93.png\")
diverges if ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=15fc21fbf11d330e31b17a30ec130d0a.png\")
, then series converges to the sum ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=ef72e9111e8935ea5352511600ee7836.png\")
.
![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=99fb9247d80ce1c575ee4d4393f2e30b.png\")
The total time taken by the ball to bounce up as it does to fall is ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=fbf9018cbd00928d185ff78d4082665e.png\")
.
![\"\"](\"http://www.mathskey.com/userfiles/image/steps_images/solution.JPG\")
The total time taken by the ball to bounce up as it does to fall is .