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Power sums/Induction/Exercise
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Prove the following formulas by induction.
∑
i
=
1
n
i
=
n
(
n
+
1
)
2
,
{\displaystyle {}\sum _{i=1}^{n}i={\frac {n(n+1)}{2}}\,,}
∑
i
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n
i
2
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n
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n
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(
2
n
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6
.
{\displaystyle {}\sum _{i=1}^{n}i^{2}={\frac {n(n+1)(2n+1)}{6}}\,.}
∑
i
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1
n
i
3
=
(
n
(
n
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1
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2
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2
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{\displaystyle {}\sum _{i=1}^{n}i^{3}={\left({\frac {n(n+1)}{2}}\right)}^{2}\,.}
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