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Mathematics
Mathematics
Problem
Let
n
n
n
be a positive integer. a. (a) Evaluate
S
n
=
∑
k
=
1
n
(
4
k
−
3
)
+
5
∑
k
=
1
n
2
\displaystyle S_n=\sum_{k=1}^{n}(4k-3)+5\sum_{k=1}^{n}2
S
n
=
k
=
1
∑
n
(
4
k
−
3
)
+
5
k
=
1
∑
n
2
and express the answer in its simplest form in terms of
n
n
n
. b. (b) Hence find
S
20
S_{20}
S
20
. (Leave the final answer as an integer.)
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