Consider the following.
a1 = 8, an + 1 = 9 − an
Calculate, to four...
Consider the following.
a1 = 8, an + 1 = 9 − an
Calculate, to four decimal places, the first eight terms of the
recursive sequence.
Does it appear to be convergent?
Yes No
If so, guess the value of the limit. (If the quantity diverges,
enter DIVERGES.)
Assume the limit exists and determine its exact value. (If the
quantity diverges, enter DIVERGES.)
lim n→∞ an =
Consider the following.
a1 = 1, an + 1 =
square root (4an)...
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...
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...
Using the recursion formula an+1 = (3an - 2)^1/2, with a1 = 4/3,
do the following...
Using the recursion formula an+1 = (3an - 2)^1/2, with a1 = 4/3,
do the following by induction.
a. Show the sequence { an } is monotone increasing.
b. Show the sequence is bounded above by 2.
c. Evaluate the the limit of the sequence.
Question 3. Let a1,...,an ∈R. Prove that
(a1 + a2 + ... + an)2
/n ≤...
Question 3. Let a1,...,an ∈R. Prove that
(a1 + a2 + ... + an)2
/n ≤ (a1)2 + (a2)2 +
... + (an)2.
Question 5. Let S ⊆R and T ⊆R be non-empty. Suppose that s ≤ t for
all s ∈ S and t ∈ T. Prove that sup(S) ≤ inf(T).
Question 6. Let S ⊆ R and T ⊆ R. Suppose that S is bounded above
and T is bounded below. Let U = {t−s|t ∈ T, s...
We are given a sequence of numbers: 1, 3, 5, 7, 9, . . . and...
We are given a sequence of numbers: 1, 3, 5, 7, 9, . . . and
want to prove that the closed formula for
the sequence is an = 2n – 1.
What would the next number in the sequence be?
What is the recursive formula for the
sequence?
Is the closed formula true for
a1?
What about a2?
What about a3?
Critical Thinking
How many values would we have to check before we could be sure
that the...
Give a recursive description of the sequence of increasing even
numbers 2, 4, 6, ...
Give a recursive description of the sequence of increasing even
numbers 2, 4, 6, ...