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Mathematics
Mathematics
Problem
Evaluate the following series: a.
∑
k
=
3
17
(
2
(
k
+
1
)
2
+
3
(
4
3
)
k
)
=
\sum_{k=3}^{17} \left( 2(k+1)^2 + 3 \left( \frac{4}{3} \right)^k \right) =
∑
k
=
3
17
(
2
(
k
+
1
)
2
+
3
(
3
4
)
k
)
=
b.
[
∑
j
=
1
15
(
j
5
−
7
j
)
]
−
[
∑
m
=
1
15
(
m
5
−
9
)
]
=
[\sum_{j=1}^{15} (j^5 - 7j)] - [\sum_{m=1}^{15} (m^5 - 9)] =
[
∑
j
=
1
15
(
j
5
−
7
j
)]
−
[
∑
m
=
1
15
(
m
5
−
9
)]
=
c.
∑
k
=
1
3
(
∑
m
=
k
+
1
k
+
4
(
m
+
k
)
)
\sum_{k=1}^{3} \left( \sum_{m=k+1}^{k+4} (m+k) \right)
∑
k
=
1
3
(
∑
m
=
k
+
1
k
+
4
(
m
+
k
)
)
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