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China Contests
China Northern MO
2009 China Northern MO
1
1
Part of
2009 China Northern MO
Problems
(1)
x_n=\sqrt{x_{n-1}^2+x_{n-1}}+x_{n-1}} ,x_1=1
Source: China Northern MO 2009 p1 CNMO
12/12/2020
Sequence {
x
n
x_n
x
n
} satisfies:
x
1
=
1
x_1=1
x
1
=
1
,
x
n
=
x
n
−
1
2
+
x
n
−
1
+
x
n
−
1
{x_n=\sqrt{x_{n-1}^2+x_{n-1}}+x_{n-1}}
x
n
=
x
n
−
1
2
+
x
n
−
1
+
x
n
−
1
(
n
>
=
2
{n>=2}
n
>=
2
) Find the general term of {
x
n
x_n
x
n
}
Sequence
algebra
recurrence relation