Let a0 = 1, a1 = 2, a2 = 4, and an = an-1 + an-3...
Let a0 = 1, a1 = 2, a2 = 4, and an = an-1 + an-3 for n>=
3.
Let P(n) denote an an <= 2^n.
Prove that P(n) for n>= 0 using strong induction:
(a) (1 point) Show that P(0), P(1), and P(2) are true, which
completes
the base case.
(b) Inductive Step:
i. (1 point) What is your inductive hypothesis?
ii. (1 point) What are you trying to prove?
iii. (2 points) Complete the proof:
Let a0 = 1, a1 = 2, a2 = 4, and an = an-1 + an-3...
Let a0 = 1, a1 = 2, a2 = 4, and an = an-1 + an-3 for n>=
3.
Let P(n) denote an an <= 2^n.
Prove that P(n) for n>= 0 using strong induction:
(a) (1 point) Show that P(0), P(1), and P(2) are true, which
completes
the base case.
(b) Inductive Step:
i. (1 point) What is your inductive hypothesis?
ii. (1 point) What are you trying to prove?
iii. (2 points) Complete the proof:
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...
For the sequence 8x + 4, 7x + 3, 6x + 2, 5x +1, ... ,...
For the sequence 8x + 4, 7x + 3, 6x + 2, 5x +1, ... ,
a. Identify the next 3 terms.
b. Is the sequence arithmetic or geometric? How do you know?
c. Find the explicit and recursive formulae for this
sequence.
d. Write out the sum formula for the first 20 terms and
evaluate.
e. Write your process to part (d) in Sigma Notation.
1) Suppose a1, a2, a3, ... is a sequence of integers such that
a1 =1/16 and...
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...