ryteich19
ryteich19
22-10-2017
Mathematics
contestada
Evaluate the series 50 + 10 + 2 + . . .
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WojtekR
WojtekR
22-10-2017
It is a sum of geometric series, where first term [tex]a_1=50[/tex] and common ratio:
[tex]r=\dfrac{a_2}{a_1}=\dfrac{10}{50}=\dfrac{1}{5}[/tex]
so:
[tex]S=50+10+2+\ldots=\dfrac{a_1}{1-r}=\dfrac{50}{1-\frac{1}{5}}=\dfrac{50}{\frac{4}{5}}=\dfrac{50\cdot5}{4}=\dfrac{250}{4}=\boxed{62.5}[/tex]
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