Check all of the following that are true for the series
∑n=1∞(n−8)cos(nπ)/(n^2).
Converge, diverge, integral test,...
Check all of the following that are true for the series
∑n=1∞(n−8)cos(nπ)/(n^2).
Converge, diverge, integral test, comparison test, limit
comparison, ratio test, and alternation test.
Check all of the following that are true for the series
∑n=1∞(n−3)cos(n*π)n^2
A. This series converges B. This series diverges C. The integral
test can be used to determine convergence of this series. D. The
comparison test can be used to determine convergence of this
series. E. The limit comparison test can be used to determine
convergence of this series. F. The ratio test can be used to
determine convergence of this series. G. The alternating series
test can be...
Determine if the following series converge or diverge. If it
converges, find the sum.
a. ∑n=(3^n+1)/(2n) (upper limit of sigma∞, lower limit is
n=0)
b.∑n=(cosnπ)/(2) (upper limit of sigma∞ , lower limit is n=
1
c.∑n=(40n)/(2n−1)^2(2n+1)^2 (upper limit of sigma ∞ lower limit
is n= 1
d.)∑n = 2/(10)^n (upper limit of sigma ∞ , lower limit of sigma
n= 10)
1. Given the series:
∞∑k=1 2/k(k+2)
does this series converge or diverge?
converges
diverges
If the series converges, find the sum of the series:
∞∑k=1 2/k(k+2)=
2. Given the series:
1+1/4+1/16+1/64+⋯
does this series converge or diverge?
diverges
converges
If the series converges, find the sum of the series:
1+1/4+1/16+1/64+⋯=
2. Determine if the following series converge or diverge.
Justify your answers, citing any appropriate tests for convergence
that you use.
(a) sigma^infinity_n=1 n + 2/(n^5/3 + n + 5 )
(b) sigma^infinity_n=1 (1 − 1/ n)^n ^2
1. Find all the values of x such that the given series would
converge.
∞∑n=1 (3x)^n/n^11
The series is convergent
from x = , left end included (enter Y
or N):
to x = , right end included (enter Y
or N):
2. Find all the values of x such that the given series would
converge.
∞∑n=1 5^n(x^n)(n+1) /(n+7)
The series is convergent
from x= , left end included (enter Y or N):
to x= , right end included (enter Y or...
Prove series 2, (-1/2), (2/9), (-1/8) is convergent by the
alternating series test and find the number of terms required to
estimate the sum of the series with an error of less than 0.05
Use an appropriate comparison test to determine the
convergence/divergence of the following series:
a.)∑ n= (1)/(√n−1) (Upper limit of the sigma is ∞ and the lower
limit of the sigma is n=2)
b.) ∑ n=n(n+1)/(n^2+1) (n-1) (Upper limit of sigma is ∞ and the
lower limit of sigma is n=2)
c.) ∑ n= cos^2(n)/ (n^3/2) (Upper limit of sigma is ∞ and the
lower limit of sigma is n=1)
d.) ∑ 5^n/(√n4^n) (Upper limit of sigma is ∞ and the...
Which of the following is a true statement? (Check all that
apply.)A technological improvement isolated to one sector can
indirectly result in more production in all other sectors.All points on the PPF are productively efficient.It is possible for a point to be allocatively efficient without
being productively efficient.PPFs slope down for the same reason that the demand curve slopes
down.