# Limits vs Summation

Calculus Level 3

$\large \displaystyle\lim_{n\to\infty}\left(\dfrac{n^2b+1}{2n^2a-1}\right)=\ 1$

Suppose for real numbers $$a,b$$, we have the limit above.

What is the value of $$\displaystyle\sum_{n=1}^{\infty}\left(\dfrac{ab}{a^2+b^2}\right)^n \ ?$$

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