Primer recorrido : 10m
segundo recorrido (bote) : 10 (3 / 4)
Tercer recorrido (de caída) : 10 (3 / 4)
Cuarto recorrido (bote) : 10 (3 / 4)²
Quinto recorrido (caída) : 10 (3 / 4)²
.
En el 2n recorrido : <img src="https://tex.z-dn.net/?f=10%283%2F4%29%5En" />
en el (2n + 1) recorrido : <img src="https://tex.z-dn.net/?f=10%283%2F4%29%5En" />
.
Sumatoria de recorridos :
<img src="https://tex.z-dn.net/?f=S%3D10%2B%5Cleft%5B20%5Cleft%28%5Cdfrac%7B3%7D%7B4%7D%5Cright%29%2B20%5Cleft%28%5Cdfrac%7B3%7D%7B4%7D%5Cright%29%5E2%2B20%5Cleft%28%5Cdfrac%7B3%7D%7B4%7D%5Cright%29%5E3%2B%5Ccdots%20%5Cright%5D%5C%5C%20%5C%5C%20%5C%5C%0AS%3D10%2B20%5Cleft%5B%5Cleft%28%5Cdfrac%7B3%7D%7B4%7D%5Cright%29%2B%5Cleft%28%5Cdfrac%7B3%7D%7B4%7D%5Cright%29%5E2%2B%5Cleft%28%5Cdfrac%7B3%7D%7B4%7D%5Cright%29%5E3%2B%5Ccdots%20%5Cright%5D%5C%5C%20%5C%5C" /> = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Suma de progresiones geométricas
sea la progresión geométrica<img src="https://tex.z-dn.net/?f=r%2Cr%5E2%2Cr%5E3%2C%5Chdots%2Cr%5En" /> su suma viene dada por : <img src="https://tex.z-dn.net/?f=%5Cboxed%7BS_n%3D%5Cdfrac%7Br-r%5E%7Bn%2B1%7D%7D%7B1-r%7D%7D" />
Suma de series geométricas infinitas
si<img src="https://tex.z-dn.net/?f=%7Cr%7C%5C%20%5Ctextless%20%5C%201" /> entonces <img src="https://tex.z-dn.net/?f=%5Cboxed%7BS%3Dr%2Br%5E2%2Br%5E3%2B%5Ccdots%3D%5Cdfrac%7Br%7D%7B1-r%7D%7D" /> = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Como 3 / 4 < 1, entonces podemos aplicar la fórmula
<img src="https://tex.z-dn.net/?f=S%3D10%2B20%5Cleft%5B%5Cleft%28%5Cdfrac%7B3%7D%7B4%7D%5Cright%29%2B%5Cleft%28%5Cdfrac%7B3%7D%7B4%7D%5Cright%29%5E2%2B%5Cleft%28%5Cdfrac%7B3%7D%7B4%7D%5Cright%29%5E3%2B%5Ccdots%20%5Cright%5D%5C%5C%20%5C%5C%20%5C%5C%0AS%3D10%2B20%5Cleft%28%5Cdfrac%7B3%2F4%7D%7B1-3%2F4%7D%5Cright%29%5C%5C%20%5C%5C%0A%5Cboxed%7BS%3D70%7D" />.