Chapter 10: Infinite Sequences and Series - Section 10.10 - The Binomial Series and Applications of Taylor Series - Exercises 10.10 - Page 633: 50

$ x^2 e^{-2x}$

Recall the Taylor series for : $ e^x=1+x+\dfrac{x^2}{2!}+.....\dfrac{x^n}{n!}...; |x| \lt \infty $ Now, $=x^2-2x^3+\dfrac{2^2 x^4}{2!}-\dfrac{x^2}{2!}-\dfrac{2^3 x^5}{3!}..$ or, $=x^2(1-2x+\dfrac{(2x)^2}{2!}-\dfrac{(2x)^3}{3!}+....)$ or, $=x^2 e^{-2x}$