Binomial Theorem and Sequences: High School Math Concepts, Cheat Sheet of Mathematics

A concise overview of the binomial theorem and sequences, including arithmetic progressions (ap) and geometric progressions (gp). It covers key formulas for finding the nth term and the sum of series, along with special series and the general term of (a+x)^n. The document also includes notes on mid-terms and greatest coefficients, making it a useful resource for high school students studying these topics. It also covers exponential and logarithmic series.

Typology: Cheat Sheet

2022/2023

Available from 12/17/2025

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BINOYIAL THEOREM,
SEQ
UENCES
AP:
* a,
atd,
a+
2d...
*
tn
at
(n-i)ol
*
If
a,b,
c are
in
AP
2b-
atc
*
a,
ar,
ar2
+ f
a,
b,
e are
in
GP
SERIES
arithmetic
Acometris
Sn
2at
(n-Da
=
2[a]
a(r")
r-l
-
all-r)
(-r
if
rl
if
r<I
an
if
r=|
¢SERIES
SPECIAL SERIES
1+2+3
+.
...
n =
n(n+1)
)+2+
3+...
n*_
nln+2n
+)
GENERAL
TERM
OF
(a+ay
T+n,
at
NOTE:
*nlo
2
n
MIDE
TERM
OF
(aty)
T+iE
n
even
GREATEST
OEFFICIENTS
n
n’even
nlnl
xnCn
nodd
pf2

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AP:BINOYIAL^ THEOREM,^ SEQ^ UENCES *** (^) tnIfa, atd,a,b,at (n-i)ol ca+ are^ 2d... in AP

  • a, ar,2b- ar2^ atc
  • f a, b,e are in GP SERIESarithmetic AcometrisSn

2at (n-Da

=

2[a]

a(r")r-l

  • all-r)(-r ifif^ rl r<I an if r=|

¢SERIESSPECIAL SERIES )+2+1+2+3 3+...^ +.^ ...^ nn*_^ =^ nln+2nn(n+1)^ +) GENERALNOTE:T+n, TERM OF (a+ayat *nlo

2

n

MIDET+iE TERM OF (aty)n even

GREATESTn OEFFICIENTSn’even

nlnl xnCn nodd

infinite 3comctric serits

(0+) --nzt^ n(n-)^ n(n-)(n-)s, (0-z) -

e

= |-n^ %t^ n^ (n+1) exponentiae =|+ (^) 1! t

logorithmiclog ( +z)

  • )+nz^ +^ n^ (n+)

binoial heoren

  • 2! (^22) 2!

2!

n(n), 2 n(n+)) (nt)+...

2!

n2!(n+)22! n(nt)ntz)+.. 3!^3 3! loq (1-2)^ =^ -z-Z 2

3! +4!

- z- +

4!^4 + 4! 4 +...

(a-a)(a+b)^ - gnGz""'nlo^ a"b°^ t^ nc,^ tn,^ a"b'+nG^ z""a'nls^ a""L²+....^ "*a'+...^ nGn^ nGz,r^ a^ b^