Answer
$$
\sum_{n=1}^{\infty} e^{-n} \cos n
$$
The function
$$
f(x)=e^{-x} \cos x
$$
is not positive for $x\geq1$ . So, it follows that $f$ does not satisfy the conditions for the Integral Test.
Work Step by Step
$$
\sum_{n=1}^{\infty} e^{-n} \cos n
$$
The function
$$
f(x)=e^{-x} \cos x
$$
is not positive for $x\geq1$ . So, it follows that $f$ does not satisfy the conditions for the Integral Test.
