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3
[IMONST2 2022 Primary #3] sum of n(n+3)
[IMONST2 2022 Primary #3] sum of n(n+3)
Source:
July 4, 2023
arithmetic
algebra
induction
Problem Statement
Prove that
1
⋅
4
+
2
⋅
5
+
3
⋅
6
+
⋯
+
n
(
n
+
3
)
=
n
(
n
+
1
)
(
n
+
5
)
3
1\cdot 4 + 2\cdot 5 + 3\cdot 6 + \cdots + n(n+3) = \frac{n(n+1)(n+5)}{3}
1
⋅
4
+
2
⋅
5
+
3
⋅
6
+
⋯
+
n
(
n
+
3
)
=
3
n
(
n
+
1
)
(
n
+
5
)
for all positive integer
n
n
n
.
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