Hi guys... this problem is really annoying me(adsbygoogle = window.adsbygoogle || []).push({});

How to find:

[tex]\displaystyle{\sum_{k=0}^{n}\frac{1}{2^k+3^k}}[/tex]

I can clearly see that it converges

[tex]\frac{1}{3^k+3^k}<\frac{1}{2^k+3^k}<\frac{1}{2^k+2^k}[/tex]

[tex]\sum_{k=0}^{\infty}\frac{1}{3^k+3^k}<\sum_{k=0}^{\infty}\frac{1}{2^k+3^k}<\sum_{k=0}^{\infty}\frac{1}{2^k+2^k}[/tex]

[tex]\frac{1}{2}\sum_{k=0}^{\infty}\frac{1}{3^k}<\sum_{k=0}^{\infty}\frac{1}{2^k+3^k}<\frac{1}{2}\sum_{k=0}^{\infty}\frac{1}{2^k}[/tex]

[tex]\frac{1}{2}\frac{1}{1-1/3}<\sum_{k=0}^{\infty}\frac{1}{2^k+3^k}<\frac{1}{2}\frac{1}{1-1/2}[/tex]

[tex]\frac{3}{4}<\sum_{k=0}^{\infty}\frac{1}{2^k+3^k}<1[/tex]

But how do I find the general expression from k=0 to 'n' or even the exact value as n goes to infinity?

Thanks in advance

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# Find the general expression from k=0 to 'n'

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