Please solve fully
Determine whether the geometric series is convergent or
divergent. If it is convergent, find its sum.8 − 11 +
121
8
−
1331
64
+
Step 1
To see 8 − 11 +
121
8
−
1331
64
+ as a geometric series, we
must express it as
∞
ar n − 1
n = 1
.
For any two successive terms in the geometric series
∞
ar n − 1
n = 1
, the ratio of...
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...
25. Answer these questions.
a. Is the series convergent of divergent? Why? Use any method.
Sum (upper inf, bot n=1) of (1)/(n3+5)
b. Is the series convergent of divergent? Why? Use any method.
Sum (upper inf, bot n=1) of
(-1n)(sin(1/n2))
c. Find the radius and interval of convergence. Sum (upper inf,
bot n=1) of (xn)/((4n)(n2))
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)