Points:

The term between any 2 terms in a AP/GP/HP is the mean(AM/GM/HM respectively) of the 2 terms
$If i, j are independent variables in \sum \sum (T_{i} \times T_{j}) then, \sum \sum (T_{i} \times T_{j}) = (\sum T_{i}) (\sum T_{j}), this can be generalized to any number of independent variables$
$If the general term can be expressed as T_{n} = \pm (V (n) - V (n - 1)) then the series is telescopic i.e., \sum T_{n} = \pm (V (n) - V (0))$
$For n = V (n) - V (n - a), \sum T_{n} = V (n) + V (n - 1) + ... + V (n - a + 1) - [V (0) + V (- 1) + ... + V (- a + 1)]$

Trivia:

∅ represents an empty set
Set minus can be represented as either ∖ or −
If a polynomial appear to have more roots than its degree then all the coefficients are 0
$When differences of consecutive terms form an AP (in a QP) then, the general term is given by T_{n} = a n^{2} + b n + c$
$When differences of consecutive terms form a GP then, the general term is given by T_{n} = a r^{n} + b$
And rule is used to find number of ways to perform one task and another
Or rule is used to find number of ways to perform one task xorOne or the other but not both another
∏ is product of n terms in a sequence and ∑ represents sum of n terms in a sequence
$a | b means "a divides b"$