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))
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...
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+⋯=
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