"A ball is dropped vertically from a height h onto a flat surface. After the
nth bounce it returns to a height h/(3^n)
Find the total distance travelled
by the ball."
My question is Why is the sum to infinity used as opposed to Sum to n?
Total Distance = h + 2*Sum of Geometric progression (to infinity)
h + 2*h/3 / 1-1/3
h + 2h/3 *3/2 = h + h = 2h
At first I did sum to infinity purely as it would give a neater answer excluding the variable n. Then I thought this might not be accurate as energy losses will mean the ball eventually comes to a stop. But the question was posed in the maths section of a paper. So should an assumption be, the ball suffers no energy loss and thus keeps on bouncing for ever?
How can I deduce that the sum to infinity must be used from the question?
nth bounce it returns to a height h/(3^n)
Find the total distance travelled
by the ball."
My question is Why is the sum to infinity used as opposed to Sum to n?
Total Distance = h + 2*Sum of Geometric progression (to infinity)
h + 2*h/3 / 1-1/3
h + 2h/3 *3/2 = h + h = 2h
At first I did sum to infinity purely as it would give a neater answer excluding the variable n. Then I thought this might not be accurate as energy losses will mean the ball eventually comes to a stop. But the question was posed in the maths section of a paper. So should an assumption be, the ball suffers no energy loss and thus keeps on bouncing for ever?
How can I deduce that the sum to infinity must be used from the question?