# Total Distance Travelled by a Ball Dropped Comes to Rest

A ball is dropped from a height of $16$ metres onto a timber floor and bounces. After each bounce, the maximum height reached by the ball is $80 \%$ of the previous maximum height. Thus, after it first hits the floor, it reaches a height of $12.8$ metres before […]

# Sum of an Infinite Geometric Series

To examine the sum of all the terms of an infinite geometric sequence, we need to consider $S_n = \dfrac{u_1(1-r^n)}{1-r}$ when $n$ gets very large. If $\left|r\right|>1$, the series is said to be divergent and the sum infinitely large.For instance, when $r=2$ and $u_1=1$;$S_\infty=1+2+4+8+\cdots$ is infinitely large. If $\left|r\right|<1$, or $-1 \lt r \lt 1$, […]