Sequences: Group 2 - Exponential and Geometric Sequences | Problems #4 and #9

Group 2 — Exponential and geometric sequences Problems #4, #9 Problem Sequence #4 \(\displaystyle a_n=\frac{n^4}{2^n}\) #9 \(\displaystyle a_n=\frac{4^n}{5^n}\) Common strategy: Compare exponential growth rates. #4: An exponential with base greater than 1 eventually grows faster than any fixed polynomial power. #9: Combine powers using \(\frac{a^n}{b^n}=(\frac ab)^n\). Rules to learn: Exponential growth and geometric limits.