Test the series for convergence or divergence.

infinity(sigma)n=1
(-1)^(n-1)/ (2n+5)


lim 1/(2n+5) = ?
n-->infinity

Note that this is an alternating series. In order for an alternating series to converge, we require that:
(a) The non-alternating part forms a monotonically decreasing sequence.
(b) The non-alternating part goes to zero as n --> infinity.

Since 1/[2(n + 1) + 5] < 1/(2n + 5) and:
lim (n-->infinity) 1/(2n + 5) = 0,

we see that the series converges.

I hope this helps!