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1962 Polish MO Finals
1
1
Part of
1962 Polish MO Finals
Problems
(1)
sum 1/a_k a_{k+1}=(n-1)/a_1a_n
Source: Polish MO Finals 1962 p1
8/30/2024
Prove that if the numbers
a
1
,
a
2
,
…
,
a
n
a_1, a_2,\ldots, a_n
a
1
,
a
2
,
…
,
a
n
(
n
n
n
- natural number
≥
2
\geq 2
≥
2
) form an arithmetic progression, and none of them is zero, then
1
a
1
a
2
+
1
a
2
a
3
+
…
+
1
a
n
−
1
a
n
=
n
−
1
a
1
a
n
.
\frac{1}{a_1a_2} + \frac{1}{a_2a_3} + \ldots + \frac{1}{a_{n-1}a_n} = \frac{n-1}{a_1a_n}.
a
1
a
2
1
+
a
2
a
3
1
+
…
+
a
n
−
1
a
n
1
=
a
1
a
n
n
−
1
.
algebra
Arithmetic Progression
Sum