Which equation could be used to calculate the sum of the geometric series?

Asked by maham237 @ 27/12/2020 in Mathematics viewed by 334 People

Which equation could be used to calculate the sum of the geometric series? 1/3 + 2/9 + 4/27 + 8/81 + 16/243?

Answered by maham237 @ 27/12/2020

Answer: $S_{n}$ = a( $\frac{1-r^{n}} {1-r}$ ) when r $\leq$ 1

and $S_{n}$ = $a(\frac{r^{n}-1} {r-1})$ when r $\geq$ 1

Explanation:

where a is first term of geometric series

r = common ratio of geometric series

n= number of terms of geometric series

In the given series a= $\frac{1}{2}$

r= $\frac{2}{3}$

n=5

So, substituting the values in the equation for r $\leq$ 1

you will get the required result

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