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A geometric series is the sum of a finite number of terms in a geometric sequence. Just like the arithmetic series, we also have geometric series formulas to help us with that.

Related concepts: Pascal's triangle, Binomial theorem, Introduction to infinite series, Convergence & divergence of geometric series ,

• the sum of n terms of a geometric series:

${s_n} = \frac{{{t_1}\;\left( {{r^n} - 1} \right)}}{{r - 1}}$

$=\frac{r \cdot t_{n}-t_{1}}{r-1}$

${s_n} = \frac{{{t_1}\;\left( {{r^n} - 1} \right)}}{{r - 1}}$

$=\frac{r \cdot t_{n}-t_{1}}{r-1}$

- 1.
**Geometric series formula:${s_n} = \frac{{{t_1}\;\left( {{r^n} - 1} \right)}}{{r - 1}}$**

Determine the sum of the first twelve terms of the geometric series: 5 – 10 + 20 – 40 + … . - 2.
**Geometric series formula: $s_{n}=\frac{r \cdot t_{n}-t_{1}}{r-1}$**

Determine the sum of the geometric series: 8 + 2 + $\frac{1}{2}$ + …. + $\frac{1}{{512}}$ . - 3.A tennis ball is dropped from the top of a building 15 m high. Each time the ball hits the ground, it bounces back to only 60% of its previous height. What is the total vertical distance the ball has travelled when it hits the ground for the fifth time?

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