A ball is thrown vertically to a height of $625$ meters from ground. Each time it hits the ground it bounces $\frac{2}{5}$ of the height it fell in the previous stage. How much will the ball travel during the first $20$th bounces? How can we derive a formula for finding this?
2026-05-15 02:16:45.1778811405
distance travelled after nth bounce
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Formula for $n$ bounces for your question: $$\displaystyle 625\left(1+2\sum_{k=1}^{n} \left(\frac{2}{5}\right)^k\right)$$