Binomial Theorem

Formulas are organized based on their importance in the CAT exam.
1 Approximation of Cube Root
2 Expansion of $$(1+x)^{-1/2}$$
3 Approximation of Reciprocal
4 Number of Terms in a Multinomial Expansion
5 Binomial Theorem for Negative Exponent
6 Coefficient of a Particular Power in a Product
7 Sum of k(k-1) times Binomial Coefficients
8 Middle Term(s) in Expansion
9 Sum of k² times Binomial Coefficients
10 Sum of Squares of Binomial Coefficients
11 Alternating Sum of Coefficients
12 Expansion of $$(1+x)^{1/2}$$
13 General Term in Negative Binomial Expansion
14 Approximation of Reciprocal Square Root
15 General Term in Binomial Expansion
16 Binomial Theorem Expansion
17 Sum of k times Binomial Coefficients
18
19 General Term with Negative Sign
20 Sum of Coefficients
21 Binomial Expansion by Substitution
22 Weighted Sum of Binomial Coefficients
23 Difference of Two Binomial Expansions
24 Generalized Binomial Coefficient
25 Higher Factorial-Moment Identity
26 Generalized Binomial Theorem
27 Coefficient of a Particular Term
28 General Term with Variables
29 General Term in (A x^p + B x^q)^n
30 Binomial Coefficient as a Product
31 Ratio of Two General Terms
32 Expansion of $$(a-x)^n$$
33 Consecutive Binomial Coefficient Relation
34 Sum of $$r^2$$ Times Binomial Coefficient
35 Alternating Sum of Coefficients
36 Independent Term in a Product of Binomials
37 Two Equal Greatest Terms
38 Binomial Expansion of $$(1+x)^n$$
39 Product of Equidistant Terms
40 Pascal's Triangle
41 Sum of Even-Powered Terms
42 Sum of Two Binomial Expansions
43 Sum of Coefficients at Alternate Positions
44 Hockey-Stick Identity
45 Approximation of Square Root
46 Number of Terms
47 Expansion of $$(1+x)^{-n}$$
48 Approximation of Negative Powers
49 Divisibility by $$(x-1)$$
50 Coefficient of $$x^r$$
51 Sum of Multinomial Coefficients
52 Sum of $$r^34$ Times Binomial Coefficient
53 Product Relation of Consecutive Coefficients
54 Middle Term
55 Greatest Binomial Coefficient
56 Coefficient of a Particular Power
57 Binomial Theorem
58 Coefficient of a Particular Term in a Trinomial
59 Sum of Odd-Power Coefficients
60 Sum of Even-Power Coefficients
61 Coefficient of $$x^r$$ in a Product
62 Coefficient of $$x^r$$ in $$(1+x)^m(1+x)^n$$
63 Binomial Expansion of $$(1-x)^n$$
64 Product of Binomial Coefficients
65 Binomial Coefficient
66 Multinomial Coefficient
67 Binomial Expansion for Large Powers
68 Greatest Term in a Binomial Expansion
69 Vandermonde's Identity
70 Multinomial Theorem
71 Expansion of $$(1+x)^m$$ for Positive Integer $$m$$
72 Ratio of Two Binomial Coefficients
73 Binomial Coefficient as a Polynomial
74 First Term and Last Term
75 Sum of Terms Equidistant from Ends
76 Binomial Expansion of $$(a+b)^n+(a-b)^n$$
77 Expansion of $$(1-x)^{-n}$$
78 Pascal's Identity
79 Divisibility Using Binomial Expansion
80 Sum of Binomial Coefficients
81 Condition for a Greatest Term
82 Expansion of $$(a+x)^n$$
83 Approximation Using Binomial Theorem
84 Expansion of (1 - x)^{-n}
85 Binomial Expansion of $$(a+b)^n-(a-b)^n$$
86 Binomial Expansion with Three Terms
87 Sum of Squares of Binomial Coefficients
88 Constant Term Condition
89 Remainder Using Binomial Expansion
90 Symmetry of Binomial Coefficients
91 Independent Term
92 Sum of Odd-Powered Terms
93 Last Digits Using Binomial Expansion
94 Second Weighted Sum
95 Sum of Consecutive Binomial Coefficients