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Mathematics
Mathematics
Problem
Determine the value of the constant
k
k
k
if
lim
n
→
∞
∑
i
=
1
n
(
k
(
1
+
2
i
n
)
2
)
⋅
2
n
=
24.
\lim_{n\to\infty}\sum_{i=1}^{n}\left(k\Bigl(1+\tfrac{2i}{n}\Bigr)^{2}\right)\cdot\tfrac{2}{n}=24.
n
→
∞
lim
i
=
1
∑
n
(
k
(
1
+
n
2
i
)
2
)
⋅
n
2
=
24.
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