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

Question

Quizplus · Accepted Answer

The series $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 1.001 } }$ is similar to the harmonic series but converges because the exponent is greater than 1. Using the Integral Test, the sum is approximately the integral from 1 to infinity of $x^{-1.001}$, which evaluates to a value between 1000 and 1001.

According to the Estimates Found in the Justification for the Integral