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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.

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A number increased by 27 is 233. Find the number.
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206

Step-by-step explanation:

233 - 27 = 206

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15=5+4(2d-3). How to you write this out? And what is the answer for d?
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Pencils come in packages of 10.Erasers come in packages of 12. Phillips wants to purpose the smallest number of pencils and eras
balandron [24]

Answer:

The answer to your question is:

Packages of pencils = 6

Packages of erasers = 5

Step-by-step explanation:

Data

Pencils = 10/package

Erasers = 12 / package

Process

Find the least common factor of 10 and 12

                                    10     12     2

                                     5       6     2

                                     5       3     3

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LCF = 2 x 2 x 3 x 5 = 60

Finally divide 60 by the number of pencils or erasers in each package

Packages of pencils = 60/10 = 6

Packages of erasers = 60/12 = 5

                                                 

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Happy studying!
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