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Mathematics
Problem
Let
n
n
n
be a positive integer and
Δ
r
=
∣
r
2
+
r
r
+
1
r
−
2
2
r
2
+
3
r
−
1
3
r
3
r
−
3
r
2
+
2
r
+
3
2
r
−
1
2
r
−
1
∣
and
\Delta_r = \begin{vmatrix} r^2+r & r+1 & r-2 \\ 2r^2+3r-1 & 3r & 3r-3 \\ r^2+2r+3 & 2r-1 & 2r-1 \end{vmatrix} \text{ and}
Δ
r
=
r
2
+
r
2
r
2
+
3
r
−
1
r
2
+
2
r
+
3
r
+
1
3
r
2
r
−
1
r
−
2
3
r
−
3
2
r
−
1
and
∑
r
=
1
n
Δ
r
=
a
n
2
+
b
n
+
c
,
find the value of
a
+
b
+
c
.
\sum_{r=1}^{n} \Delta_r = an^2 + bn + c, \text{ find the value of } a+b+c.
r
=
1
∑
n
Δ
r
=
a
n
2
+
bn
+
c
,
find the value of
a
+
b
+
c
.
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