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September 5, 2015
Posted by **Shawna** on Wednesday, March 19, 2014 at 12:05pm.

A) 2

B) 3

C) 4

D) 5

E) 6

- Math - PreCalc (12th Grade) -
**Steve**, Wednesday, March 19, 2014 at 12:07pmstart checking. How about showing some of your own ideas on further problems? I can do them - the goal is for you to work on them, eh?

- Math - PreCalc (12th Grade) -
**Shawna**, Wednesday, March 19, 2014 at 12:08pmHonestly, i don't get any of them..

- Math - PreCalc (12th Grade) -
**Steve**, Wednesday, March 19, 2014 at 12:16pmit asks for the first natural number ...

the natural numbers are 1,2,3,...

So, start trying them:

n=1: (2n-1) = 1

1 <= 4*1-1

1 <= 3? yes

n=2: (2n-1) = 3

1+3 <= 4*2-1

4 <= 7? yes

n=3: (2n-1) = 5

1+3+5 <= 4*3-1

9 <= 11? yes

n=4: (2n-1) = 7

1+3+5+7 <= 4*4-1

16 <= 15? NO

Or, you can solve the inequality. As you can see,

1+3+5+...+(2n-1) = n^2

So, we want to see where

x^2 <= 4n-1

x^2 - 4n + 1 <= 0

this parabola has a root at 2+√3 = 3.7

So, as long as x <= 3.7, x^2 <= 4n-1

The first natural number greater than 3.7 is 4.

- Math - PreCalc (12th Grade) -
**Shawna**, Wednesday, March 19, 2014 at 12:21pmThank you!! you really are helping me alot.