MathDB
Problems
Contests
National and Regional Contests
Iran Contests
Pre-Preparation Course Examination
2012 Pre-Preparation Course Examination
2
convergent sequences
convergent sequences
Source: Iran PPCE 2012-Analysis exam-P2
February 14, 2012
limit
real analysis
real analysis unsolved
Problem Statement
Suppose that
lim
n
→
∞
a
n
=
a
\lim_{n\to \infty} a_n=a
lim
n
→
∞
a
n
=
a
and
lim
n
→
∞
b
n
=
b
\lim_{n\to \infty} b_n=b
lim
n
→
∞
b
n
=
b
. Prove that
lim
n
→
∞
1
n
(
a
1
b
n
+
a
2
b
n
−
1
+
.
.
.
+
a
n
b
1
)
=
a
b
\lim_{n\to \infty}\frac{1}{n}(a_1b_n+a_2b_{n-1}+...+a_nb_1)=ab
lim
n
→
∞
n
1
(
a
1
b
n
+
a
2
b
n
−
1
+
...
+
a
n
b
1
)
=
ab
.
Back to Problems
View on AoPS