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
erica [24]
3 years ago
9

Prove that n!<n^n for n≥2​

Mathematics
1 answer:
frutty [35]3 years ago
7 0

Answer:

Step-by-step explanation:

Hello,

We will prove it by induction.

Step 1 - for n=2

2!=2*1=2

2^2=4

and 2 < 4 so this is true for n=2

Step2 - We assume that this is true for k and we have to prove it for k+1.

Induction hypothesis is k!

(k+1)!=(k+1)k!

We use the induction hypothesis and we we can write that

(k+1)!=(k+1)k!

so, we prove it for k+1

Step 3- conclusion

for n >= 2 we just proved that n!

You might be interested in
Use the FOIL method to evaluate the expression
In-s [12.5K]
So u multiply each term in the first parentheses by each term in the second parentheses.

√5 √5 + 6√5-3√5 - 3x6
Now you multiply the numbers which will get u:
5+6√5 - 3√5 - 18
Then subtract:
-13 +3√5 that’s your answer
7 0
3 years ago
Find the greatest common factor of 15x^2 y^3 and -20x^3yz
maxonik [38]
5x^2y

5 is the largest number to go in evenly. And the terms are limited to those. 
6 0
3 years ago
Hey can yalls help me plz ​
katen-ka-za [31]

Answer:

4

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
I am crying fo help<br>5.<br>6.<br>7.<br>8.
bixtya [17]
3*567=1701 because you have to muply
6 0
3 years ago
Read 2 more answers
Find the first three iterates of the function f(z) = 2z + (3 - 2i) with an initial value of z0 = 5i.
Agata [3.3K]
3 because the 2z minus the 3 gives you 1 rounded
4 0
4 years ago
Read 2 more answers
Other questions:
  • Assuming that a sample (n = 504) has a sample standard deviation of 2.26, what is the upper bound of a 95% confidence interval i
    15·1 answer
  • At the market, Ms. Winn bought 3/4 lb of grapes and 5/8 lb of cherries. How many ounces of grapes did Ms. Winn buy?
    11·2 answers
  • What is another way to write the ratio 3 to 10 ?
    15·1 answer
  • Please help!<br><br> Questions above<br><br>(the options I choose are incorrect for sure)
    10·2 answers
  • Any help at all is greatly appreciated??!!!
    12·1 answer
  • Which expression is equivalent to 6^-3?<br> 6^3<br> 3^6<br> 3sqrt6<br> (1/6)^3
    13·2 answers
  • In the blank, type the greatest common factor of these two numbers.
    7·1 answer
  • Use the given information to prove that RSU=TSV
    7·1 answer
  • You are shopping for school supplies. You want to buy 8 notebooks for $1.50 each. Show how you can use the distributive property
    11·1 answer
  • In how many ways may one A, three B’s, two C’s, and one F be distributed among seven
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!