# Proof of Sum of Geometric Series by Mathematical Induction

Considerations of Sum of Geometric Series The sum of geometric series is defined using r, the common ratio and n, the number of terms. The common could be any real numbers with some exceptions; the common ratio is 1 and 0. If the common ratio is 1, the series becomes the sum of constant numbers, […]

# 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 […]

# Geometric Sequence and Geometric Mean

Geometric Sequence Definition Geometric Sequences are sequences where each term is obtained by multiplying the preceding term by a certain constant factor, which is often called $\textit{common ratio}$. A geometric sequence is also referred to as a $\textit{geometric progression}$. David expects $10$% increase per month to deposit to his account. A $10$% increase per month […]