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Problems
If
(
1
+
x
)
n
=
C
0
+
C
1
x
+
C
2
x
2
+
C
3
x
3
+
⋯
+
C
n
x
n
,
prove that
\text{If } (1+x)^n = C_0 + C_1 x + C_2 x^2 + C_3 x^3 + \dots + C_n x^n, \text{ prove that}
If
(
1
+
x
)
n
=
C
0
+
C
1
x
+
C
2
x
2
+
C
3
x
3
+
⋯
+
C
n
x
n
,
prove that
…
Mathematics
Problem
If
(
1
+
x
)
n
=
C
0
+
C
1
x
+
C
2
x
2
+
C
3
x
3
+
⋯
+
C
n
x
n
,
prove that
\text{If } (1+x)^n = C_0 + C_1 x + C_2 x^2 + C_3 x^3 + \dots + C_n x^n, \text{ prove that}
If
(
1
+
x
)
n
=
C
0
+
C
1
x
+
C
2
x
2
+
C
3
x
3
+
⋯
+
C
n
x
n
,
prove that
C
1
2
+
2
C
2
2
+
3
C
3
2
+
⋯
+
n
C
n
2
=
(
2
n
−
1
)
!
(
n
−
1
)
!
2
C_1^2 + 2C_2^2 + 3C_3^2 + \dots + nC_n^2 = \frac{(2n-1)!}{(n-1)!^2}
C
1
2
+
2
C
2
2
+
3
C
3
2
+
⋯
+
n
C
n
2
=
(
n
−
1
)
!
2
(
2
n
−
1
)!
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