- #1
Dell
- 590
- 0
i am given te series:
∞
Σ(-1)n-1/{n+50*cos(n)}
n=1
1st thing i check is
lim |an| = 0
n->∞
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,
an>an+1 ==> not true for this series since -1<cos(n)<1 i cannot know if the denominator of an is bigger or smaller than that of an+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 an/bn=K ( not 0, not \infty) then an, bn both diverge/converge
if i take bn=(-1)n-1/n which i know converges(conditionally)
therefore
lim an/bn= 1
n->\∞
so an converges
which is the right answer BUT i think that this comaprison is only for positive series,
how else can i solve alternating series
∞
Σ(-1)n-1/{n+50*cos(n)}
n=1
1st thing i check is
lim |an| = 0
n->∞
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,
an>an+1 ==> not true for this series since -1<cos(n)<1 i cannot know if the denominator of an is bigger or smaller than that of an+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 an/bn=K ( not 0, not \infty) then an, bn both diverge/converge
if i take bn=(-1)n-1/n which i know converges(conditionally)
therefore
lim an/bn= 1
n->\∞
so an converges
which is the right answer BUT i think that this comaprison is only for positive series,
how else can i solve alternating series