Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
To obtain the alternating sum
∑
k
=
0
n
(
−
1
)
k
(
n
k
)
\displaystyle \sum_{k=0}^{n} (-1)^k {n\choose k}
k
=
0
∑
n
(
−
1
)
k
(
k
n
)
directly from the expansion of
(
a
+
b
)
n
(a+b)^n
(
a
+
b
)
n
, which choice of
(
a
,
b
)
(a,\,b)
(
a
,
b
)
is appropriate? a)
a
=
1
,
b
=
1
a=1,\;b=1
a
=
1
,
b
=
1
b)
a
=
−
1
,
b
=
1
a=-1,\;b=1
a
=
−
1
,
b
=
1
c)
a
=
1
,
b
=
−
1
a=1,\;b=-1
a
=
1
,
b
=
−
1
d)
a
=
0
,
b
=
1
a=0,\;b=1
a
=
0
,
b
=
1
Browse the problem library