- #1

- 590

- 0

_{ ∞}

Σ(-1)

^{n-1}/{n+50*cos(n)}

^{n=1}

1st thing i check is

*lim |a*

n->∞

_{n}| = 0n->∞

so i know that the series might converge and might diverge,

since this is a series with an alternating sign, i checked with lebniz rule,

*a*==> not true for this series since -1<cos(n)<1 i cannot know if the denominator of a

^{n}>a_{n+1}^{n}is bigger or smaller than that of a

_{n+1}

so using leibniz i cannot prove conditional convergence, (and i know from the answer that this series converges),

can i use the second comparative test, ie

if a

_{n}/b

_{n}=K ( not 0, not \infty) then a

_{n}, b

_{n}both diverge/converge

if i take b

_{n}=(-1)

^{n-1}/n which i know converges(conditionally)

therefore

*lim a*

n->\∞

_{n}/b_{n}= 1n->\∞

so a

_{n}converges

which is the right answer BUT i think that this comaprison is only for positive series,

how else can i solve alternating series