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1995 IMC
8
IMC 1995 Problem 8
IMC 1995 Problem 8
Source: IMC 1995
February 19, 2021
Summation
real analysis
Problem Statement
Let
(
b
n
)
n
∈
N
(b_{n})_{n\in \mathbb{N}}
(
b
n
)
n
∈
N
be a sequence of positive real numbers such that
b
0
=
1
b_{0}=1
b
0
=
1
,
b
n
=
2
+
b
n
−
1
−
2
1
+
b
n
−
1
b_{n}=2+\sqrt{b_{n-1}}-2\sqrt{1+\sqrt{b_{n-1}}}
b
n
=
2
+
b
n
−
1
−
2
1
+
b
n
−
1
. Calculate
∑
n
=
1
∞
b
n
2
n
.
\sum_{n=1}^{\infty}b_{n}2^{n}.
n
=
1
∑
∞
b
n
2
n
.
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