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Ok, so the image below is a scan of my work on this problem, I think I got as far as I could, but don't know how to proceed, or if I have even been doing this correctly thus far.

Thank you for the help!

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\begin{align*} \sum_{k=1}^{n^2} \frac{4^{2k+1}}{7^{-k+4}} = \sum_{k=1}^{n^2}\frac{4}{7^4} (7 \cdot 16)^k\\ &= \frac{4}{7^4} \times 7 \cdot 16 \times \frac{(7 \cdot 16)^{n^2} - 1}{7 \cdot 16 -1} \end{align*} Similar computation for the other sum.

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  • $\begingroup$ I don't get how you got that. Can you please explain? $\endgroup$ May 11, 2017 at 22:44
  • $\begingroup$ Nevermind, I figured it out, just an algebra rule I had forgotten. Thank you! I did the same thing for the other summation and I believe I now have a valid answer. $\endgroup$ May 12, 2017 at 0:42

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