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

Question

Find the smallest value of N that will make the inequality hold for all n > N.
-$$\frac { 10 ^ { n } } { n ! } < 10 ^ { - 3 }$$
A) 31
B) 30
C) 20
D) 21

Quizplus · Accepted Answer

By calculating an appropriate number of terms, determine if the series converges or diverges. If it converges, find the limit $\mathrm { L }$ and the smallest integer $\mathrm { N }$ such that $\left| \mathrm { a } _ { \mathrm { n } } - \mathrm { L } \right| < 0.01$ for $\mathrm { n } \geq \mathrm { N }$; otherwise indicate divergence.

Find the Smallest Value of N That Will Make the Inequality