(a) Does the series X∞ k=1 (−1)^k+1 /k + √ k converge? (b) Essay
part. Which tests can be applied to determine the convergence or
divergence of the above series. For each test explain in your own
words why and how it can be applied, or why it cannot be applied.
(i) (2 points) Alternating Series Test. (ii) Absolute Convergence
Test
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+⋯=
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. 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...
1. Can you understand the emotions of another
person?
Do you ever find your emotions challenging to understand? Give
example.
2. Research suggests that happiness has many good
consequences, but other research describrs the benefits of
defensive pessimism. Do these lines of research contradict each
other, or could they both be right? Explain your answer.
Find as many programming languages as possible which fit the
following categories. When you find a language which fits the
category, indicate the following information:
The name of the language
The year the language was released
A sample bit of code to prove that the language belongs to the
given category.
For full marks, you must find at least two languages for each
category. To make the assignment more interesting, extra points
will be awarded to the person who finds...
Find the charge on the capacitor in an LRC-series circuit at t =
0.05 s when L = 0.05 h, R = 3 Ω, C = 0.008 f, E(t) = 0 V, q(0) = 4
C, and i(0) = 0 A. (Round your answer to four decimal places.)
C
Determine the first time at which the charge on the capacitor is
equal to zero. (Round your answer to four decimal places.) s