Page 260 - Calculus Workbook For Dummies

244 Part IV: Integration and Infinite Series

3
Q. Does ! n 1 - 1 converge or diverge? If your teacher is a stickler for rigor, you
n 1 n can do the following: Plugging in 3
=
/ 1 3
1
A. It diverges. produces 1 - 3 m , which is 1 , and that
0
c
You can answer this question with equals 1 — you’re done. (Note that 1 0
common sense if your calc teacher is not one of the forms that gives you a
allows such a thing. As n gets larger and L’Hôpital’s Rule problem — see Chapter
3
1 1 1, ! 1
n
larger, 1 - n increases and gets closer 12.) Because lim 1 - n = n 1 - n
n " 3
=
and closer to one. And when you take diverges. n 1
any root of a number like 0.9, it gets
bigger — and the higher the root index,
1
the bigger the answer is. So 1 - n has
n
to get larger as n increases and thus
1
lim 1 - n cannot possibly equal zero.
n
n " 3
The series, therefore, diverges by the nth
term test.

3
2
3
1. Does ! 2 n - 9 n - 8 converge or 2. Does ! 1 converge or diverge?
n
2
=
n 1 5 n + 20 n + 12 n 1
=
diverge? Solve It
Solve It