Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
The geometric series
1
1
+
x
=
∑
n
=
0
∞
(
−
1
)
n
x
n
\displaystyle\frac{1}{1+x}=\sum_{n=0}^{\infty}(-1)^{n}x^{n}
1
+
x
1
=
n
=
0
∑
∞
(
−
1
)
n
x
n
converges for
∣
x
∣
<
1
|x|<1
∣
x
∣
<
1
. Determine the Maclaurin series (general term) for
ln
(
1
+
x
)
\ln(1+x)
ln
(
1
+
x
)
and state its radius of convergence.
Browse the problem library