Prove that n!<n^n for n≥2

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

We use the induction hypothesis and we we can write that

so, we prove it for k+1

Step 3- conclusion

for n >= 2 we just proved that

56

step-by-step explanation:

this is a direct variation proportion. y = kx

y is the total amount due, k is the constant of variation, and x is the number of texts sent.

plug in the 3.20 and the 16 to solve for the "k". this is the constant of proportionality. it is the value that will not change.

3.20 = k(16). solving you get $.20 per text.

the equation would then be y = .20x