1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
natulia [17]
3 years ago
13

Question 31 pts Prove the statement is true using mathematical induction: 2n-1 ≤ n! Use the space below to write your answer. To

make the < symbol, you might want to use the < with the underline feature.
Mathematics
1 answer:
Sladkaya [172]3 years ago
4 0

Answer:

P(3) is true since 2(3) - 1 = 5  < 3! = 6.  

Step-by-step explanation:

Let P(n) be the proposition that 2n-1 ≤ n!. for n ≥ 3

Basis: P(3) is true since 2(3) - 1 = 5  < 3! = 6.  

Inductive Step: Assume P(k) holds, i.e., 2k - 1 ≤ k! for an arbitrary integer k ≥ 3. To show that P(k + 1) holds:

2(k+1) - 1 = 2k + 2 - 1

≤ 2 + k! (by the inductive hypothesis)

= (k + 1)! Therefore,2n-1 ≤ n! holds, for every integer n ≥ 3.

You might be interested in
Please answer correctly
Afina-wow [57]

Answer:

2nd and 4th options

Step-by-step explanation:

both answers begin with a fixed point drawn with a straight line through a point that continues on by showing an arrow

3 0
2 years ago
Read 2 more answers
What is d if <img src="https://tex.z-dn.net/?f=%5Cfrac%7B3d-2%7D%7B8%7D%20%3D%20-d%2B16%5Cfrac%7B1%7D%7B4%7D" id="TexFormula1" t
Harlamova29_29 [7]

Answer: d=12

Step-by-step explanation:

\displaystyle\\\frac{3d-2}{8} =-d+16\frac{1}{4} \\\\\frac{3d-2}{8} =-d+\frac{16*4+1}{4} \\\\\frac{3d-2}{8} =-d+\frac{64+1}{4} \\\\\frac{3d-2}{8} =-d+\frac{65}{4}

Multiply both parts of the equation by 8:

\displaystyle\\3d-2=(-d+\frac{65}{4} )(8)\\\\3d-2=-8d+65*2\\\\3d-2=-8d+130\\\\3d-2+2=-8d+130+2\\\\3d=-8d+132\\\\3d+8d=-8d+132+8d\\\\11d=132\\

Divide both parts of the equation by 11:

d=12

8 0
1 year ago
What is the simplified fraction is equal to 0.53 ?
Anna007 [38]
.53= 53/100

53/100 cannot be simplified so the answer is 53/100
4 0
3 years ago
Before a bag of flour can be sold, it must be 40 kilograms but can be within 0.5
Serjik [45]

Answer:

The minimum acceptable weight of the flour bag is 39.5 kg,

and its maximum acceptable weight is 40.5 kg

Step-by-step explanation:

Notice that the selling weight of the bag to be sold (x) needs to differ from 40 kg at most 0.5 kg. Therefore, we can write the following inequality:

|x-40|\leq 0.5

The inequality can be solve once we remove the absolute value symbol, and solve for the unknown "x". Recall that in order to solve it, we need to consider the two possible cases:

a) that the expression within the absolute value symbol is larger than or equal to zero, and b) that the expression is less than zero.

a) If x-40\geq 0 then its absolute value is equal to itself (x-40), and when we remove the absolute value symbols, we get:

x-40\leq 0.5\\x\leq 0.5+40\\x\leq 40.5\,\,kg

which means that the weigh "x" of the flour bag should be smaller or equal than 40.5  kg

b) If x-40, then the absolute value of this is its opposite : -x+40, and the inequality becomes:

-x+40\leq 0.5\\40\leq 0.5+x\\40-0.5\leq x\\39.5\leq x

which means that the weight of the flour bag must be larger than or equal to 39.5 kg

So, the minimum acceptable weight of the flour bag is 39.5 kg, and the maximum acceptable weight is 40.5 kg

6 0
3 years ago
Mr.miller spends an hour and a half working in his garden. which number line could show the time Mr.miller spends working in his
IgorLugansk [536]

Answer: 3:00 4:00

Step-by-step explanation:

I’m to lazy to say why but trust me

7 0
3 years ago
Other questions:
  • There are 18 bulls and 45 cows on a ranch. If 4 more bulls and 4 more cows were added,will the ratio of bulls to cows remain the
    9·2 answers
  • How do you know how to solve algebraic equations in the correct order?
    10·1 answer
  • How would I complete this?
    13·1 answer
  • Which is smaller 1/6 or 1/5
    8·2 answers
  • Triangle a need to be rotated in a 90 degrees counterclockwise
    13·1 answer
  • HELP please i'll give brainliest I only have until 3 to finish this
    5·2 answers
  • My smart people help me love yall! ^^
    6·1 answer
  • Is 2/5 a rational number?
    7·2 answers
  • X÷-1.2= -0.3 i need help with this asap pls and thank you ​
    9·1 answer
  • The KM values for the reaction of chymotrypsin with 2 substrates are given below. Which substrate is likely to give a higher val
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!