Sequences & Series

Formulas are organized based on their importance in the CAT exam.
1 Sum of Squares of First n Natural Numbers
2 Sum of First n Natural Numbers
3 Relation Between AM and HM
4 Geometric Progression
5 Sum of an AP
6 Sum of First $$n$$ Odd Numbers
7 Arithmetic Mean of Terms of an AP
8 Sum of Reciprocals of Consecutive Products
9 Sum of Consecutive Integers from $$m$$ to $$n$$
10 Sum of Consecutive Even Numbers
11 Arithmetic-Geometric Series Sum
12 Telescoping Series: Partial Fractions Example
13 Sum of a Binomial Expansion
14 Last Term of an AP
15 Sum of First n Odd Natural Numbers
16 Convergence of a GP
17 Recurrence for an AP
18 Geometric Mean (GM) of n Numbers
19 Geometric Progression in Terms of Two Terms
20 Arithmetic Mean
21 Sum of Consecutive Odd Numbers
22 Three Numbers in GP
23 Inserting Arithmetic Means
24 Arithmetic Progression in Terms of Two Terms
25 Sum of a Finite Geometric Series in Alternative Form
26 AM-GM for Multiple Positive Numbers
27 Geometric Progression: Sum to Infinity
28 Monotonicity of a GP
29 Sum of Terms in a GP with General Starting Index
30 Common Ratio of a GP
31 Middle Term of an AP
32 Three Numbers in AP and GP
33 Sum of a GP Using First and Last Terms
34 Harmonic Progression
35 Common Difference
36 Geometric Mean of Terms of a GP
37 Relation Between AM, GM and HM
38 Harmonic Mean
39 Four Numbers in AP
40 Middle Term of a GP
41 Average of Terms in an Arithmetic Progression
42 Infinite Geometric Progression
43 Infinite GP Remainder
44 Sum of a Finite GP
45 Sum of First $$n$$ Even Numbers
46 Geometric Mean
47 Inserting Geometric Means
48 Sum of a GP Starting from the $$m$$th Term
49 Infinite GP with Alternating Terms
50 Properties of an AP
51 Relation Between Equidistant Terms of an AP
52 Infinite Arithmetic-Geometric Progression
53 Relation Between Equidistant Terms of a GP
54 Sequence
55 Sequence Defined by a Recurrence
56
57 Recurrence for a GP
58 Partial Fractions in Telescoping Sums
59 Sum of Fourth Powers
60 Sum of Squares of First $$n$$ Natural Numbers
61 Sum of a General Linear Sequence
62 Weighted Binomial Sum
63 Telescoping Series
64 Change of Index in Summation
65 Sum of Binomial Coefficients
66 Sum of Fourth Powers
67 Sum of Cubes of First $$n$$ Natural Numbers
68 Sum of Products of Consecutive Natural Numbers
69 Arithmetic Mean–Geometric Mean Relation
70 Arithmetic Progression
71 Monotonicity of an AP
72 Geometric Progression: Sum of n Terms (Finite)
73 Arithmetic-Geometric Progression
74 Sigma Notation
75 Arithmetic Progression: Sum of n Terms
76 Sum of First $$n$$ Natural Numbers
77 Geometric Progression: General Term
78 Arithmetic Mean (AM) of n Numbers
79 Last Term of a GP
80 Infinite GP as a Limit
81 Arithmetic Progression: General Term
82 Sum of a Binomial Expansion
83 Sum of Terms in an AP with General Starting Index
84 Harmonic Progression: Definition
85 Harmonic Mean (HM) of n Numbers
86 Sum of Cubes of First n Natural Numbers
87 Three Numbers in AP