According to the Estimates Found in the Justification for the Integral

Multiple Choice

According to the estimates found in the justification for the Integral Test, the sum of the series $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 1.001 } }$ must lie between what two values?

A) 101 & 102
B) 102 & 103
C) 999 & 1000
D) 1001 & 1002
E) 1002 & 1003
F) 1000 & 1001
G) 99 & 100
H) 100 & 101