Find the smallest value of N that will make the inequality hold for all n > N.
- $\frac { n ^ { 2 } } { 2 ^ { n } } < 10 ^ { - 3 }$

Question

Find the smallest value of N that will make the inequality hold for all n > N.
-$$\frac { n ^ { 2 } } { 2 ^ { n } } < 10 ^ { - 3 }$$
A) 17
B) 20
C) 19
D) 18

Quizplus · Accepted Answer

The inequality $\frac{n^2}{2^n} < 10^{-3}$ can be solved through trial and error or by using logarithms and calculus to approximate the value of $n$. By testing values, we find that for $n = 19$, the inequality holds true, making $n = 19$ the smallest integer value for which the inequality is satisfied for all $n > N$.

Find the Smallest Value of N That Will Make the Inequality