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Bogdan Stan
2013 Bogdan Stan
4
Nice application of Cesaro-Stolz
Nice application of Cesaro-Stolz
Source:
July 5, 2020
Cesaro-Stolz
real analysis
Seqeunce
Sequence
Problem Statement
Let be a sequence
(
x
n
)
n
≥
1
\left( x_n \right)_{n\ge 1}
(
x
n
)
n
≥
1
having the property that
lim
n
→
∞
(
14
(
n
+
2
)
x
n
+
2
−
15
(
n
+
1
)
x
n
+
1
+
n
x
n
)
=
13.
\lim_{n\to\infty } \left( 14(n+2)x_{n+2} -15(n+1)x_{n+1} +nx_n \right) =13.
n
→
∞
lim
(
14
(
n
+
2
)
x
n
+
2
−
15
(
n
+
1
)
x
n
+
1
+
n
x
n
)
=
13.
Show that
(
x
n
)
n
≥
1
\left( x_n \right)_{n\ge 1}
(
x
n
)
n
≥
1
is convergent and calculate its limit. Cosmin Nițu
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