Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
A power series representation of
1
1
+
x
2
\displaystyle \frac{1}{1+x^{2}}
1
+
x
2
1
that converges for
∣
x
∣
<
1
|x|<1
∣
x
∣
<
1
is
∑
n
=
0
∞
(
−
1
)
n
x
2
n
\sum_{n=0}^{\infty}(-1)^n x^{2n}
∑
n
=
0
∞
(
−
1
)
n
x
2
n
. Find a power series representation for
arctan
x
\arctan x
arctan
x
satisfying
arctan
0
=
0
\arctan 0=0
arctan
0
=
0
, and determine the interval of convergence.
Browse the problem library