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South Korea USCM
2019 Korea USCM
5
5
Part of
2019 Korea USCM
Problems
(1)
evaluate sum of partial products
Source: 2019 South Korea USMC P5
8/13/2020
A sequence
{
a
n
}
n
≥
1
\{a_n\}_{n\geq 1}
{
a
n
}
n
≥
1
is defined by a recurrence relation a_1 = 1, a_{n+1} = \log \frac{e^{a_n}-1}{a_n} And a sequence
{
b
n
}
n
≥
1
\{b_n\}_{n\geq 1}
{
b
n
}
n
≥
1
is defined as
b
n
=
∏
i
=
1
n
a
i
b_n = \prod\limits_{i=1}^n a_i
b
n
=
i
=
1
∏
n
a
i
. Evaluate an infinite series
∑
n
=
1
∞
b
n
\sum\limits_{n=1}^\infty b_n
n
=
1
∑
∞
b
n
.
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