Question

1. (24 pts.) For which integer values of the constant k does the sequence {a1, a2, a3, . . .} defined by

an = (5n^k + 3)/(3n^k + 5)

converge? For those values of k, compute the limit of the sequence {a1, a2, a3, . . .}.

Answer #1

2. Exercise 19 section 5.4. Suppose that a1, a2, a3, …. Is a
sequence defined as follows:
a1=1 ak=2a⌊k/2⌋ for every integer k>=2.
Prove that an <= n for each integer n >=1.
plzz send with all the step

Let A = (A1, A2, A3,.....Ai) be defined as a sequence containing
positive and negative integer numbers.
A substring is defined as (An, An+1,.....Am) where 1 <= n
< m <= i.
Now, the weight of the substring is the sum of all its
elements.
Showing your algorithms and proper working:
1) Does there exist a substring with no weight or zero
weight?
2) Please list the substring which contains the maximum weight
found in the sequence.

1) Suppose a1, a2, a3, ... is a sequence of integers such that
a1 =1/16 and an = 4an−1. Guess a formula for an and prove that your
guess is correct.
2) Show that given 5 integer numbers, you can always find two of
the numbers whose difference will be a multiple of 4.
3) Four cats and five mice form a row. In how many ways can they
form the row if the mice are always together?
Please help...

Consider the following sequence: 0, 6, 9, 9, 15, 24, . . .. Let
the first term of the sequence, a1 = 0, and the second, a2 = 6, and
the third a3 = 9. Once we have defined those, we can define the
rest of the sequence recursively. Namely, the n-th term is the sum
of the previous term in the sequence and the term in the sequence 3
before it: an = an−1 + an−3. Show using induction...

A'1(x)=2A1(x)-A2(x)-A3(x)
A'2(x)=-A1(x)+2A2(x)-A3(x)
A'3(x)=-A1(x)-A2(x)+2A3(x)
with A1(0) = 0, A2(0) = 1, and A3(0) = 5 being initial
values
solve linear differential equations

Consider the sequence defined recursively by
an+1 = (an + 1)/2 if an is an odd number
an+1 = an/2 if an is an even number
(a) Let a0 be equal to the last digit in your student number,
and compute a1, a2, a3, a4.
(b) Suppose an = 1, and find an+4.
(c) If a0 = 4, does limn→∞ an exist?

. Consider the sequence defined recursively as a0 = 5, a1 = 16
and ak = 7ak−1 − 10ak−2 for all integers k ≥ 2. Prove that an = 3 ·
2 n + 2 · 5 n for each integer n ≥ 0

Find a general term (as a function of the variable n) for the
sequence{?1,?2,?3,?4,…}={45,1625,64125,256625,…}{a1,a2,a3,a4,…}={45,1625,64125,256625,…}.
Find a general term (as a function of the variable n) for the
sequence {?1,?2,?3,?4,…}={4/5,16/25,64/125,256/625,…}
an=
Determine whether the sequence is divergent or convergent. If
it is convergent, evaluate its limit.
(If it diverges to infinity, state your answer as inf . If it
diverges to negative infinity, state your answer as -inf . If it
diverges without being infinity or negative infinity, state your
answer...

1) if a sequence is monotone decreasing and greater than 0 for
all values of n (n=1 to infinity) then the sequence must converge.
True or false?
2) In order for infinite series k=1 to infinity (ak + bk) =
series ak + series bk, both series must converge. True or
false?
3) Let f(x) be a continuous decreasing function where f(k) = ak.
If integral 1 to infinity f(x) = 5, what can we conclude about
series ak?
-series...

1. Write 3n + 1 Sequence String Generator function (1 point) In
lab5.py complete the function sequence that takes one parameter: n,
which is the initial value of a sequence of integers. The 3n + 1
sequence starts with an integer, n in this case, wherein each
successive integer of the sequence is calculated based on these
rules: 1. If the current value of n is odd, then the next number in
the sequence is three times the current number...

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