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Infinite Sum of Areas of Shrinking Astroids
Daily Problem
3 i's
Find the total area enclosed by the family of astroids
x
2
3
+
y
2
3
=
a
2
3
,
where
a
=
1
k
,
k
∈
N
.
Compute
∑
k
=
1
∞
A
(
1
k
)
.
\text{Find the total area enclosed by the family of astroids} \\\\ x^{\frac{2}{3}} + y^{\frac{2}{3}} = a^{\frac{2}{3}}, \quad \text{where } a = \frac{1}{k}, \quad k \in \mathbb{N}. \\\\ \text{Compute} \sum_{k=1}^{\infty} A\!\left(\frac{1}{k}\right).
Find the total area enclosed by the family of astroids
x
3
2
+
y
3
2
=
a
3
2
,
where
a
=
k
1
,
k
∈
N
.
Compute
k
=
1
∑
∞
A
(
k
1
)
.
Submit Answer
Submit