Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
If
I
n
I_n
I
n
denotes
∫
z
n
e
1
/
z
d
z
\int z^n e^{1/z} dz
∫
z
n
e
1/
z
d
z
, then show that
(
n
+
1
)
!
I
n
=
I
0
+
e
1
/
z
(
1
!
z
2
+
2
!
z
3
+
.
.
.
+
n
!
z
n
+
1
)
(n+1)! I_n = I_0 + e^{1/z} (1! z^2 + 2! z^3 + ... + n! z^{n+1})
(
n
+
1
)!
I
n
=
I
0
+
e
1/
z
(
1
!
z
2
+
2
!
z
3
+
...
+
n
!
z
n
+
1
)
.
Browse the problem library