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Problem 6
2021 CMC (Non-Math Major) Problem 6
2021 CMC (Non-Math Major) Problem 6
Source: 2021 CMC (Non-Math Major) Problem 6
November 25, 2022
calculus
Problem Statement
Let
x
1
=
2021
x_1=2021
x
1
=
2021
,
x
n
2
−
2
(
x
n
+
1
)
x
n
+
1
+
2021
=
0
x_n^2-2(x_n+1)x_{n+1}+2021=0
x
n
2
−
2
(
x
n
+
1
)
x
n
+
1
+
2021
=
0
(
n
≥
1
n\geq1
n
≥
1
). Prove that the sequence
x
n
{x_n}
x
n
converges. Find the limit
lim
n
→
∞
x
n
\lim_{n \to \infty} x_n
lim
n
→
∞
x
n
.
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