I have worked this problem at least 30 times and am still not getting the correct answer. Can anyone tell me where I'm wrong?
Partial sum of a geometric series:
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$$\sum_{n=1}^{\infty} \frac{8^n+3^n}{9^n}$$
for the sum formula $\frac{a}{1-r}$ I have the values for the variables as:
$a = \frac{11}{9}$
$r = \frac{73}{99}$
I found $r$ by dividing the first value of the series ($\frac{11}{9}$) by the second value of the series ($\frac{73}{81}$).
I keep getting the sum as $\frac{121}{26}$
The correct value for the sum is $\frac{17}{2}$
What am I doing wrong?
Best Answer
You will have $$\sum_{n=1}^\infty\left(\frac{8}{9}\right)^n$$ and $$\sum_{n=1}^\infty\left(\frac{1}{3}\right)^n$$ The first sum is $$8$$ and the second $$\frac{1}{2}$$