sequences and series - The sum of $1+frac 25 + frac {3}{5^2} + frac {4}{5^3}....$

Monday 22 January 2018

sequences and series - The sum of $1+frac 25 + frac {3}{5^2} + frac {4}{5^3}....$

The nth term would be
$$T_n = \frac{n}{5^{n-1}}$$

So the sum will be $$\sum T_n = 5\sum \frac{n}{5^n}$$

Can’t solve further. What’s next?

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