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Révisions Maths lycée
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Analyse Terminale
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Exercice
Révisions Maths lycée
Analyse Terminale
Level 3
1.
Montrer que
∀
(
a
,
b
)
∈
R
+
∗
,
l
n
(
a
b
)
=
l
n
(
a
)
+
l
n
(
b
)
,
l
n
(
1
a
)
=
−
l
n
(
a
)
,
l
n
(
a
b
)
=
l
n
(
a
)
−
l
n
(
b
)
.
2.
Simplifier la somme
S
=
∑
n
=
1
100
l
n
(
n
n
+
1
)
.
1.\text{ Montrer que }\forall (a,b)\in\mathbb{R}^*_+,\\ln(ab)=ln(a)+ln(b),\\ln(\frac{1}{a})=-ln(a),\\ln(\frac{a}{b})=ln(a)-ln(b).\\ \ \\2.\text{ Simplifier la somme}\\S=\sum\limits_{n=1}^{100}ln(\frac{n}{n+1}).
1.
Montrer que
∀
(
a
,
b
)
∈
R
+
∗
,
l
n
(
ab
)
=
l
n
(
a
)
+
l
n
(
b
)
,
l
n
(
a
1
)
=
−
l
n
(
a
)
,
l
n
(
b
a
)
=
l
n
(
a
)
−
l
n
(
b
)
.
2.
Simplifier la somme
S
=
n
=
1
∑
100
l
n
(
n
+
1
n
)
.
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