Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Suppose
u
1
,
u
2
,
u
3
,
…
u_1, u_2, u_3, \dots
u
1
,
u
2
,
u
3
,
…
is an arithmetic sequence. (a) Show that
2
u
1
,
2
u
2
,
2
u
3
,
…
2^{u_1}, 2^{u_2}, 2^{u_3}, \dots
2
u
1
,
2
u
2
,
2
u
3
,
…
is a geometric sequence. (b) Given that
u
3
=
−
4
u_3 = -4
u
3
=
−
4
and
u
5
=
−
10
u_5 = -10
u
5
=
−
10
, find the sum of the infinite geometric series
2
u
1
+
2
u
2
+
2
u
3
+
…
2^{u_1} + 2^{u_2} + 2^{u_3} + \dots
2
u
1
+
2
u
2
+
2
u
3
+
…
.
Browse the problem library