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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!

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7 0
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Given: ABCD is a trapezoid, m∠1=m∠2, m∠3=m∠4, AB = CD, AC ∩ BD = O <br> Prove: m∠AOD = m∠BCD
LiRa [457]
Since AB = CD the trapezoid is isosceles, which means that ∡A = ∡D

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For the properties of parallel lines (BD and AD) crossed by a transversal (BD) we have ∡3 = ∡CBD.

Now consider triangles AOD and BCD:
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T<span>he sum of the angles of a triangle must be 180°, t</span>herefore:
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6 0
4 years ago
If p(a) = 0.62, p(b) = 0.47, and p(a or<br> b.= 0.88, then p(a and<br> b.= _____
SIZIF [17.4K]
Use the identity:
P(A or B)=P(A)+P(B)-P(A and B)
Substitute given values,
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=>
P(A and B)=0.62+0.47-0.88=0.21
6 0
4 years ago
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