​ Find n,if lim(n→2)(x^n-2^n)/(x-2)=80, n ∈ N. ​

Question

Find n,if \(\lim\limits_{n \to 2}\frac{x^n-2^n}{x-2}=80\), n ∈ N.

Answer 1

Given,
\(\lim\limits_{n \to2}\frac{x^n-2^n}{x-2}=80\)

⇒ \(n.2^{n-1}=80\)

n₂ = 52

\([∵ \lim\limits_{n \to a}\frac{x^n-a^n}{x-a}=na^{n-1}]\)

∵ Value of n is 5.