Evaluate limn→∞(2nn+1)n\lim_{n \to \infty} \left(\frac{2n}{n+1}\right)^nlimn→∞(n+12n)n.
2n2^n2n diverges; the limit is +∞+\infty+∞... actually: ene^nen... let me recalculate. (2nn+1)n=(21+1/n)n=2n(1+1/n)n≈2ne(\frac{2n}{n+1})^n = (\frac{2}{1+1/n})^n = \frac{2^n}{(1+1/n)^n} \approx \frac{2^n}{e}(n+12n)n=(1+1/n2)n=(1+1/n)n2n≈e2n
e−1e^{-1}e−1
222
∞\infty∞