Question

How do you determine whether the sequence a_n=(2^n+3^n) / (2^n−3^n) converges, if so how do you find the limit?

Answer 1

You determine the limit by $\lim_{n \to \infty} a_n = -1$.

A limit in mathematics is a point at which a function approaches the output for the specified input values. Calculus and mathematical analysis depend on limits, which are also used to determine integrals, derivatives, and continuity. The concept of limit, which is founded on the idea of closeness, is largely used to give values to some functions at points when none are defined in a way that is consistent with values close by.

Divide the denominator and numerator by 3n as shown.

$\lim_{n \to \infty} a_n = \lim_{n \to \infty} \frac{2^n+3^n}{2^n-3^n\\}$

$= \lim_{n \to \infty} \frac{(\frac{2}{3})^n+1 }{(\frac{2}{3})^n-1 } \\=\frac{0+1}{0-1} \\=-1$

To learn more about limits, refer:-

brainly.com/question/12211820

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