May 5th, 2014, 06:44 AM  #1 
Senior Member Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36  Progression
Can somebody explain this to me?

May 5th, 2014, 09:10 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,640 Thanks: 2624 Math Focus: Mainly analysis and algebra 
First of all, you should find a general formula for $H_n$ in terms of $H_{n1}$ only. You know that $H_1 = 0.8H$ and $H_2 = 0.8H_1$, does that suggest anything? Next you can use this formula to find an expression for $H_n$ in terms of $H$ only. Try making a list of $H_1, H_2, H_3, ...$ in terms of $H$. See if you can spot a pattern. How does $H_n$ change as $n$ increases? Do the $H_n$ increase or decrease? Now you can solve $H_n \lt 50$ for $n$. In the last part, you have to work out the sum that you should evaluate. Be careful! For all but the first $H$, the ball travels the distance on the way up as well as the way down. The big question here is how far do you have to sum the series? 

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