The Binomial Inequality
The Binomial Inequality
The binomial inequality states that if ,,…, are real numbers with the same sign and , then . In this Demonstration, you can compare the two sides of the inequality for various values of the numbers involved when .
a
1
a
2
a
n
1+≥0
a
i
(1+)(1+)…(1+)≥1+(++…+)
a
1
a
2
a
n
a
1
a
2
a
n
n=5
A common special case of this inequality occurs when the are all the same. If we call this common value , then the inequality reads ≥1+nx. By checking the special case box on the left, you can view a plot of the two sides of this inequality and use the bottom slider to vary .
a
i
x
n
(1+x)
n