Problem 3
<=
o:p>
P=
rove if
n is an integer and ![](3D"2007prob3_files/image002.gif")
, then ![](3D"2007prob3_files/image004.gif")
<=
o:p>
[Problem submitted=
by Vin
Lee, LACC Associate Professor of Mathematics. Source: College Algebra, 7th ed=
ition,
by Larson and Hostetler.]
<=
o:p>
<=
o:p>
<=
o:p>
Solution for Prob=
lem 3:
=
I=
f n =3D 2,
then the left side of the inequality is
![](3D"2007prob3_files/image006.gif")
. Since ![](3D"2007prob3_files/image008.gif")
, the inequality is true for n =3D 2.
<=
o:p>
S=
uppose
the inequality holds for some integer ![](3D"2007prob3_files/image010.gif")
. Then ![](3D"2007prob3_files/image012.gif")
<=
sub>![](3D"2007prob3_files/image014.gif")
![](3D"2007prob3_files/image016.gif")
![](3D"2007prob3_files/image018.gif")
&=
nbsp; &nbs=
p; &=
nbsp; &nbs=
p; ![](3D"2007prob3_files/image020.gif")
.
So,=
if the
inequality is true for k, then it is true for k + 1. Therefore, according to the Axiom =
of
Mathematical Induction, the inequality is true for any positive integer.
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