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Mathematics
Problem
Evaluating Series a. Evaluate the series
36
+
64
+
100
+
144
+
⋯
+
10
,
000
36 + 64 + 100 + 144 + \dots + 10,000
36
+
64
+
100
+
144
+
⋯
+
10
,
000
b. Evaluate
∑
j
=
2
∞
∑
k
=
1
∞
(
1
2
)
j
(
1
3
)
k
\sum_{j=2}^{\infty} \sum_{k=1}^{\infty} \left(\frac{1}{2}\right)^j \left(\frac{1}{3}\right)^k
∑
j
=
2
∞
∑
k
=
1
∞
(
2
1
)
j
(
3
1
)
k
. If you rewrite this as a different, equivalent sigma expression, you must justify your reformulation.
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