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For a positive integer
MATHEMATICS · Subjective · ISC · Mathematics · Algebra · Algebra
Problem
For a positive integer
n
n
n
, simplify
2
∑
k
=
1
n
(
3
k
+
5
)
−
∑
k
=
1
n
4
k
−
1
2\displaystyle\sum_{k=1}^{n}(3k+5)\; -\; \displaystyle\sum_{k=1}^{n}4^{k-1}
2
k
=
1
∑
n
(
3
k
+
5
)
−
k
=
1
∑
n
4
k
−
1
and write your answer solely in terms of
n
n
n
.
Related theory
Geometric Progressions
Special Series
Special sums
Algebra
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