+118 Compute the sum
\(1 + \frac{1}{5} + \frac{2}{5} + \frac{2}{25} + \frac{4}{25} + \frac{4}{125} + \frac{8}{125} + \frac{8}{625} + \dots\)
+302 This sum if really a combination of 2 geometric series.
First geometric series: \(1\over{5}\),\(2\over{25}\),\(4\over{125}\), and so on
Second geometric series: \(2\over{5}\), \(4\over{25}\), \(8\over{125}\), and so on
use: \(a_1\over1-r\) formula: The sum of the first geometric series would be: \(1\over{5}\)\(\div\)\(3\over5\)=1/3
2nd would be: 2/5 \(\div\) 3/5 = 2/3
1/3+2/3 = 1
We still didn't add the first term: 1
So 1+1 = 2
+302 This sum if really a combination of 2 geometric series.
First geometric series: \(1\over{5}\),\(2\over{25}\),\(4\over{125}\), and so on
Second geometric series: \(2\over{5}\), \(4\over{25}\), \(8\over{125}\), and so on
use: \(a_1\over1-r\) formula: The sum of the first geometric series would be: \(1\over{5}\)\(\div\)\(3\over5\)=1/3
2nd would be: 2/5 \(\div\) 3/5 = 2/3
1/3+2/3 = 1
We still didn't add the first term: 1
So 1+1 = 2
