Stuck with this limit of a sum: $\lim _{n \to \infty} \left(\frac{a^{n}-b^{n}}{a^{n}+b^{n}}\right)$.

If $b > a$, divide both the numerator and denominator by $b^n$ to get: $$\lim_{n \to \infty} \frac{\frac{a^n}{b^n}-1}{\frac{a^n}{b^n}+1}=\frac{-1}{1}=-1$$


Hint: In case of $b>a$ you divide by $b^n$ In case of $a=b$ it is simply zero.

Tags:

Limits

Analysis

Calculus

Summation

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