Math  PreCalc (12th Grade)
posted by Shawna on .
What is the first natural number that causes the statement 1 + 3 + 5 +... + (2n − 1)<=4n − 1 to fail?
A) 2
B) 3
C) 4
D) 5
E) 6

start 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?

Honestly, i don't get any of them..

it asks for the first natural number ...
the natural numbers are 1,2,3,...
So, start trying them:
n=1: (2n1) = 1
1 <= 4*11
1 <= 3? yes
n=2: (2n1) = 3
1+3 <= 4*21
4 <= 7? yes
n=3: (2n1) = 5
1+3+5 <= 4*31
9 <= 11? yes
n=4: (2n1) = 7
1+3+5+7 <= 4*41
16 <= 15? NO
Or, you can solve the inequality. As you can see,
1+3+5+...+(2n1) = n^2
So, we want to see where
x^2 <= 4n1
x^2  4n + 1 <= 0
this parabola has a root at 2+√3 = 3.7
So, as long as x <= 3.7, x^2 <= 4n1
The first natural number greater than 3.7 is 4. 
Thank you!! you really are helping me alot.