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.

Step-by-step explanation:

Given that n! = n(n - 1)(n - 2)(n - 3)...2×1

We want to show that 2n - 1 ≤ n!

Since

n! = n(n - 1)(n - 2)(n - 3)...2×1

= n(n - 1)!

n! = n(n - 1)(n - 2)!

n! = (n² - n)(n - 2)!

From here obviously,

n! ≥ n

n! ≥ 2n

And

n! ≥ 2n - 1

Which implies

2n - 1 ≤ n!

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she will sew have sewn five dresses   and be 1/3 done with the sixth one in an hour.

step-by-step explanation:

3/4 of an hour=45 mins

lucy makes 1 dress per 11.25 minutes

45 mins+11.25 mins=56.25 mins

60 mins- 56.25 mins=3.75 mins

3.75 mins is 1/3 of of 11.25 mins

therefore she the other 1/3 would be part of the hour and she will have sewn 5 dresses and begun the sixth.

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