1 in a million

404
1.1.1.1 .
n-1nn \dfrac {\ln \left ( n\right) -\ln \left ( n-1\right) } {n-\left ( n-1\right) } \left ( \ln n\right).
2011 1
1+1=2 1 0 0
HappyHorse-1.0 4 HappyHorse-1.0 AI Artificial.
0405 vs4-1
1 111021.
2011 1 .
.

404
1.1.1.1 .
n-1nn \dfrac {\ln \left ( n\right) -\ln \left ( n-1\right) } {n-\left ( n-1\right) } \left ( \ln n\right).
2011 1
1+1=2 1 0 0
HappyHorse-1.0 4 HappyHorse-1.0 AI Artificial.
0405 vs4-1
1 111021.
2011 1 .
.
Here, \( a = 1, b = 1, c = -10100 \).
Calculate the discriminant: \( 1^2 - 4 imes 1 imes (-10100) = 1 + 40400 = 40401 \).
The square root of 40401 is 201.
Calculate \( n \): \( n = rac{-1 \pm 201}{2} \).
Choose the positive solution: \( n = rac{200}{2} = 100 \).
A rectangle has a length that is 3 times its width. If the perimeter is 48 meters, find the area of the rectangle.
The perimeter formula is \( 2( ext{length} + ext{width}) = 48 \).
Substitute: \( 2(3w + w) = 48 \), so \( 8w = 48 \).
The length is \( 3 imes 6 = 18 \).
Calculate the area: \( 18 imes 6 = 108 \).