36.62
Show that the sequence of Problem 36.61 is convergent.
Since the sequence is decreasing and bounded below by 0, it must converge. (In general, any bounded
monotonic sequence converges.)
36.63
Determine whether the sequence
is increasing, decreasing, or neither.
So
and the sequence is decreasing.
36.64
We know that
(0.99)" = 0. How large must n be taken so that (0.99)" < 0.001?
We must have
From a
table of common logarithms, Iog99 = 1.9956. So n(0.0044)>3, n >3/0.0044«681.7. So n should be
at least 682.
36.65
Let
For which x is f(x) defined?
INFINITE SEQUENCES
311
if
if
if