- #1
karush
Gold Member
MHB
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a. Find the common ration $r$, for an infinite series
with an initial term $4$ that converges to a sum of $\displaystyle\frac{16}{3}$
$$\displaystyle S=\frac{a}{1-r} $$ so $\displaystyle\frac{16}{3}=\frac{4}{1-r}$ then $\displaystyle r=\frac{1}{4}$
b. Consider the infinite geometric series
$\displaystyle
\frac{8}{25} + \frac{4\sqrt{5}}{25}+\frac{2}{5}+\frac{\sqrt{5}}{5}+\cdot\cdot\cdot$
c. What is the exact value of the common ratio of the series
$\frac{8}{25}\cdot r = \frac{4\sqrt{5}}{25}$ so $r=\frac{\sqrt{5}}{2}$d. Does the series converge?
not sure how to do this?
with an initial term $4$ that converges to a sum of $\displaystyle\frac{16}{3}$
$$\displaystyle S=\frac{a}{1-r} $$ so $\displaystyle\frac{16}{3}=\frac{4}{1-r}$ then $\displaystyle r=\frac{1}{4}$
b. Consider the infinite geometric series
$\displaystyle
\frac{8}{25} + \frac{4\sqrt{5}}{25}+\frac{2}{5}+\frac{\sqrt{5}}{5}+\cdot\cdot\cdot$
c. What is the exact value of the common ratio of the series
$\frac{8}{25}\cdot r = \frac{4\sqrt{5}}{25}$ so $r=\frac{\sqrt{5}}{2}$d. Does the series converge?
not sure how to do this?
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