Hello, I want to calculate the sum of this series:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\sum_{n=1}^\infty \frac{3^n+1}{4^n+2}[/tex],

I know the series converges, I only found this useful way to factor the denominator:

[tex] 4^n+2=2^{2n}+2=4^n(1+2^{-2n+1})[/tex],

now i have: [tex]\frac{3^n+1}{4^n+2}=(\frac{3^n}{4^n}+\frac{1}{4^n})(\frac{1}{1+2^{-2n+1}})[/tex],

i can calculate [tex]\sum_{n=1}^\infty \frac{3^n}{4^n}+ \sum_{n=1}^\infty \frac{1}{4^n}[/tex]but what should be done with

[tex]\frac{1}{1+2^{-2n+1}}[/tex]?

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# Calculate this sum

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