Find the Sum of the Series SUM((2^n + 1)/3^n)

Find the Sum of the Series SUM((2^n + 1)/3^n)

We write this as two infinite series which are both geometric in order to find the sum.

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Thank you:)

[orange]

Saved me 2 hours remaining to the exam, many thanks!

[sindydejesus]

thank you thank you! You explained it in such a clear way

[jeanjoelkapula]

How would check for convergence? Do you assume the original series converges because the two do?

[thiagofrias]

When we have (1/2)^n + (3/2)^n can we do the same method? One of them is divergent.

[joan]

Hello, thank you for helping others. I have one question. Say you have a random number multiplying in the denominator lets say 4. Could you take it out of the series as 1/4 and then multiply it with the sum of the series to find the final sum of the series? Dumb question but just want to make sure. Thank you!

[saiello]

I think its dangerous for mathematicians to be publishing any material on April 1st.... 🤨 😁

[Valeri]

what is the name of this method, just so I can explain this to teacher

[Bbduyg]

When is it ok to split infinant sum into 2 inf sum ?

[joshhernandez]

Sir does it converge or diverge?
I think it converges