Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
The power series for
ln
(
1
+
x
)
\ln(1+x)
ln
(
1
+
x
)
is
x
−
x
2
2
+
x
3
3
−
x
4
4
+
⋯
x-\dfrac{x^{2}}{2}+\dfrac{x^{3}}{3}-\dfrac{x^{4}}{4}+\cdots
x
−
2
x
2
+
3
x
3
−
4
x
4
+
⋯
for
−
1
<
x
≤
1
-1<x\le 1
−
1
<
x
≤
1
. For
x
=
0.6
x=0.6
x
=
0.6
, determine the least integer
n
n
n
such that using the first
n
n
n
non-zero terms yields an approximation to
ln
(
1.6
)
\ln(1.6)
ln
(
1.6
)
whose error does not exceed
10
−
5
10^{-5}
1
0
−
5
.
Browse the problem library