Question

determine whether given series converges absolutely , converges conditionally or diverges??
∑n=1∞ cosnΠ /n + 3

Answer 1

this?
\[\large \sum_{n=1}^\infty \frac{\cos(n\pi)}{n+3}\]
or this?
\[\large \sum_{n=1}^\infty \cos\left(\frac{n\pi}{n+3}\right)\]

Answer 2

upper one.

Answer 3

\[\cos n\pi=\pm 1\]

Answer 4

@waterineyes

Answer 5

@sirm3d right but what about Alternating series test..?

Answer 6

the series is alternating.

given \[\sum (-1)^{n} a_n\]
the series is

(a) absolutely convergent if \[\sum a_n\] is convergent

(b) conditionally convergent if the alternating series is convergent but the series of positive terms is divergent

(c) divergent if the alternating series is divergent.

Answer 7

\[\sum \frac{\cos(n\pi)}{n+3}=\sum(-1)^{n}\frac{1}{n+3}\]

take \[a_n=\frac{1}{n+3}\]

Answer 8

thanks buddy problem solved :)

Answer 9

yw