$\text { Use the polynomial test to determine whether the series } \frac { 1 } { 20 } + \frac { 2 } { 23 } + \frac { 3 } { 28 } + \frac { 4 } { 35 } + \frac { 5 } { 44 } \ldots$ converges or diverges.
A) The series $\frac { 1 } { 20 } + \frac { 2 } { 23 } + \frac { 3 } { 28 } + \frac { 4 } { 35 } + \frac { 5 } { 44 } \ldots$ diverges.
B) The series $\frac { 1 } { 20 } + \frac { 2 } { 23 } + \frac { 3 } { 28 } + \frac { 4 } { 35 } + \frac { 5 } { 44 } \ldots$ converges.

Question

$\text { Use the polynomial test to determine whether the series } \frac { 1 } { 20 } + \frac { 2 } { 23 } + \frac { 3 } { 28 } + \frac { 4 } { 35 } + \frac { 5 } { 44 } \ldots$ converges or diverges. 
A) The series $\frac { 1 } { 20 } + \frac { 2 } { 23 } + \frac { 3 } { 28 } + \frac { 4 } { 35 } + \frac { 5 } { 44 } \ldots$ diverges.
B) The series $\frac { 1 } { 20 } + \frac { 2 } { 23 } + \frac { 3 } { 28 } + \frac { 4 } { 35 } + \frac { 5 } { 44 } \ldots$ converges.

Quizplus · Accepted Answer

The series diverges because the terms of the series do not approach zero as n increases. The denominator grows as a polynomial function of n, but since the numerator also grows linearly with n, the terms do not decrease to 0, failing the necessary condition for convergence.

Converges or Diverges 120+223+328+435+544…\frac { 1 } { 20 } + \frac { 2 } { 23 } + \frac { 3 } { 28 } + \frac { 4 } { 35 } + \frac { 5 } { 44 } \ldots201​+232​+283​+354​+445​…

Converges or Diverges $\frac { 1 } { 20 } + \frac { 2 } { 23 } + \frac { 3 } { 28 } + \frac { 4 } { 35 } + \frac { 5 } { 44 } \ldots$