Posted by Shawna on Wednesday, March 19, 2014 at 12:05pm.
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: (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.
Thank you!! you really are helping me alot.