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Mathematics
Problem
Give a brief reason why
∑
k
=
1
n
[
k
3
−
(
k
−
1
)
3
]
=
n
3
\displaystyle\sum_{k=1}^{n}\bigl[k^{3}-(k-1)^{3}\bigr]=n^{3}
k
=
1
∑
n
[
k
3
−
(
k
−
1
)
3
]
=
n
3
.
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