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Digital Library of Mathematical Functions ID
1.2.E10
a
+
(
a
+
d
)
+
(
a
+
2
d
)
+
…
+
(
a
+
(
n
-
1
)
d
)
=
n
a
+
1
2
n
(
n
-
1
)
d
=
1
2
n
(
a
+
ℓ
)
,
𝑎
𝑎
𝑑
𝑎
2
𝑑
…
𝑎
𝑛
1
𝑑
𝑛
𝑎
1
2
𝑛
𝑛
1
𝑑
1
2
𝑛
𝑎
ℓ
{\displaystyle{\displaystyle a+(a+d)+(a+2d)+\dots+(a+(n-1)d)=na+\tfrac{1}{2}n(% n-1)d=\tfrac{1}{2}n(a+\ell),}}
Constraint(s)
Symbols List
n
𝑛
{\displaystyle{\displaystyle n}}
: nonnegative integer
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