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Guichard-Combinatorics-Graph-Theory
· Problem 1.3.11
Fundamentals
Mathematics — Probability · binomial-coefficients
Problem
Use
(
x
+
1
)
n
=
∑
i
=
0
n
(
n
i
)
x
i
(x+1)^n = \sum_{i=0}^{n} \binom{n}{i} x^i
(
x
+
1
)
n
=
∑
i
=
0
n
(
i
n
)
x
i
to find a simple expression for
∑
i
=
1
n
i
(
n
i
)
x
i
−
1
\sum_{i=1}^{n} i \binom{n}{i} x^{i-1}
∑
i
=
1
n
i
(
i
n
)
x
i
−
1
. Then find a simple expression for
∑
i
=
1
n
i
(
n
i
)
\sum_{i=1}^{n} i \binom{n}{i}
∑
i
=
1
n
i
(
i
n
)
.
Related theory
General Term And Binomial Coefficients
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