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...
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
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))
Find the values of p for which the series is convergent
(a) Σ(n=2 to ∞) 1/n(ln n)^p
(b) Σ(n=2 to ∞) n(1+n^2)^p
HINT: Use the integral test to investigate both