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Nicolae Coculescu
2004 Nicolae Coculescu
1
Limit involving the harmonic sequence as exponent
Limit involving the harmonic sequence as exponent
Source:
December 14, 2019
Sequences
series
limits
harmonic series
calculus
Problem Statement
Calculate
lim
n
→
∞
(
e
1
+
1
/
2
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1
/
3
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⋯
+
1
/
n
+
1
/
(
n
+
1
)
−
e
1
+
1
/
2
+
1
/
3
+
⋯
+
1
/
n
)
.
\lim_{n\to\infty } \left( e^{1+1/2+1/3+\cdots +1/n+1/(n+1)} -e^{1+1/2+1/3+\cdots +1/n} \right) .
lim
n
→
∞
(
e
1
+
1/2
+
1/3
+
⋯
+
1/
n
+
1/
(
n
+
1
)
−
e
1
+
1/2
+
1/3
+
⋯
+
1/
n
)
.
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