Note (Basic strategy for testing convergence):
As a general rule, check . If
, the series is divergent. If try convergent tests as suggested next.
try Integral test.
Root test is useful, if it is series to find root of
Using limit comparison test, determine the convergence/ divergence of the following series:
. If 
, the series is divergent. 
try convergent tests as suggested next. 
is a decreasing sequence of positive terms, such that 
for some function 
is a rational function, or is some root of 
, try limit comparison test. 
has factorial/ powers of 
root of 
.
.
(Hint 
glows more slowly than 
for every 
) 
