← Topic 1 · Algebra
AMC 10/12 · Cheatsheet
Topic 1 · Algebra
Chapter 2 · Sequences & series
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Arithmetic sum
S
n
=
n
2
(
a
1
+
a
n
)
S_n = \tfrac{n}{2}(a_1 + a_n)
S
n
=
2
n
(
a
1
+
a
n
)
Geometric sum
S
n
=
a
1
r
n
−
1
r
−
1
(
r
≠
1
)
S_n = a_1\tfrac{r^n-1}{r-1}\;(r\neq1)
S
n
=
a
1
r
−
1
r
n
−
1
(
r
=
1
)
Infinite geometric
S
∞
=
a
1
1
−
r
(
∣
r
∣
<
1
)
S_\infty = \tfrac{a_1}{1-r}\;(|r|<1)
S
∞
=
1
−
r
a
1
(
∣
r
∣
<
1
)