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Evaluate the series \(\dfrac{1}{3^1}+\dfrac{4}{3^2}+\dfrac{7}{3^3}+\dfrac{10}{3^4}+\cdots\)

 

The sum of a certain infinite geometric series is 2. The sum of the squares of all the terms is 3. Find the common ratio.

 Feb 18, 2019
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1)    ∑[ (3n -2) / 3^n, n, 1,∞] =5/4

 

2) 

See the answer here by Max Wong:

https://web2.0calc.com/questions/the-sum-of-a-certain-infinite-geometric-series-is#r4

 Feb 18, 2019

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