Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
The series
∑
k
=
1
∞
(
−
1
)
k
+
1
(
1
2
)
k
k
\displaystyle \sum_{k=1}^{\infty}(-1)^{k+1}\frac{\left(\tfrac12\right)^k}{k}
k
=
1
∑
∞
(
−
1
)
k
+
1
k
(
2
1
)
k
converges to
ln
(
3
2
)
\ln\!\left(\tfrac32\right)
ln
(
2
3
)
. What is the smallest value of
N
N
N
that guarantees the partial sum
S
N
S_N
S
N
differs from
ln
(
3
2
)
\ln\!\left(\tfrac32\right)
ln
(
2
3
)
by less than
0.0001
0.0001
0.0001
? a)
N
=
10
N=10
N
=
10
b)
N
=
9
N=9
N
=
9
c)
N
=
13
N=13
N
=
13
d)
N
=
14
N=14
N
=
14
Browse the problem library