Question:
Find the sum of each of the following infinite series :
$8+4 \sqrt{2}+4+2 \sqrt{2}+\ldots . \infty$
Solution:
It is Infinite Geometric Series.
Here, a=8
$r=\frac{4 \sqrt{2}}{8}=\frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}}$
The formula used: Sum of an infinite Geometric series $=\frac{\mathrm{a}}{1-\mathrm{r}}$
$\therefore S u m=\frac{8}{1-\frac{1}{\sqrt{2}}}=\frac{8 \sqrt{2}}{\sqrt{2}-1}$
Sum $=\frac{8 \sqrt{2}}{\sqrt{2}-1}$
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