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) 18
D) 19

Quizplus · Accepted Answer

To find the smallest N, we need to solve the inequality $\frac{n^2}{2^n} < 10^{-3}$. By testing values, we find that for n = 19, $\frac{19^2}{2^{19}} \approx 0.000724$, which is less than $10^{-3}$. For n = 18, $\frac{18^2}{2^{18}} \approx 0.00137$, which is greater than $10^{-3}$. Therefore, the smallest N is 19.

Find the Smallest Value of N That Will Make the Inequality