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...
1) The twelfth term of an arithmetic sequence is 118, and the
eighth term is 146....
1) The twelfth term of an arithmetic sequence is 118, and the
eighth term is 146. Find the nth term. (3 points)
2) A partial sum of a geometric sequence is given. Find the sum.
(3 points)
3) Determine wether the given infinite geometric series is
convergent or divergent. If the series is convergent, then find its
sum. (4 points)
a) b)
Consider a sequence defined recursively as X0=
1,X1= 3, and Xn=Xn-1+
3Xn-2 for n ≥ 2....
Consider a sequence defined recursively as X0=
1,X1= 3, and Xn=Xn-1+
3Xn-2 for n ≥ 2. Prove that Xn=O(2.4^n) and
Xn = Ω(2.3^n).
Hint:First, prove by induction that 1/2*(2.3^n) ≤ Xn
≤ 2.8^n for all n ≥ 0
Find claim, base case and inductive step. Please show step and
explain all work and details
Consider the sequence defined recursively by
an+1 = (an + 1)/2 if an is an odd...
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?
3. Consider the following property: for any ε>0, there exists
N∈N so that whenever n≥N,|u_n+1−u_n|<ε.
What...
3. Consider the following property: for any ε>0, there exists
N∈N so that whenever n≥N,|u_n+1−u_n|<ε.
What is the difference between this property and the definition
of a Cauchy sequence?
Find a convergent sequence which has this property.
Find a divergent sequence which has this property. (Hint: can
you think of a function f(x) which grows to infinity very
slowly? Then try a_n=f(n).