Question

can you please show all the steps thank you...

Prove by induction that 3n < 2^{n} for all
n ≥ ______. (You should figure out what number goes in the
blank.)

I know that the answer is n>= 4, nut I need to write the steps for induction

Answer #1

Show all the steps...
Prove by induction that 3n < 2n for all
n ≥ ______. (You should figure out what number goes in the
blank.)

Please note n's are superscripted.
(a) Use mathematical induction to prove that 2n+1 +
3n+1 ≤ 2 · 4n for all integers n ≥ 3.
(b) Let f(n) = 2n+1 + 3n+1 and g(n) =
4n. Using the inequality from part (a) prove that f(n) =
O(g(n)). You need to give a rigorous proof derived directly from
the definition of O-notation, without using any theorems from
class. (First, give a complete statement of the definition. Next,
show how f(n) =...

Prove the following using induction:
(a) For all natural numbers n>2, 2n>2n+1
(b) For all positive integersn,
1^3+3^3+5^3+···+(2^n−1)^3=n^2(2n^2−1)
(c) For all positive natural numbers n,5/4·8^n+3^(3n−1) is
divisible by 19

Please show all the steps..thankyou
Use strong induction to show any amount of postage ≥ ___________
can be made using 5 cent and 7 cent stamps. (You should fill in the
blank with the smallest value that works.)

Prove or disprove: Can a symmetric matrix be necessarily
diagonalizable?
Please show clear steps. Thank you.

Please show all steps and work no how you got answer thank
you!
Please no script! Some people have bad script hand writing
please write normal ;[
How many 6 digit numbers can you form by rearranging 769543 in
different order?
How many ways can you form committee of 11 consisting of 6
Americans and 5 Russians out of 8 Americans and 6 Russians?
Find the present value of $3000 due at the end of 11years at 10%
per year...

Prove that a tree with n node has exactly n-1 edges. Please show
all steps. If it connects to Induction that works too.

Please show all steps thank you.
Determine the smallest n such that there exists nonisomorphic
graphs of order n with the same degree sequence. Justify your
answer.

prove that 2^2n-1 is divisible by 3 for all natural numbers n ..
please show in detail trying to learn.

Please show all steps, thank you!
a) Verify that the functions below solve the system:
x(t) = c1e^5t + c2e^-t
y(t) = 2c1e^5t - c2e^-t
Do not solve the system
dx/dt = x + 2y
dy/dt = 4x +3y
b) Solve the system using Operator D elimination. Write the
answer both in scalar and vector form. Please show all steps!
dx/dt = x + 2y
dy/dt = 4x + 3y

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