PROGRESSIONS - Important Notes/Formulae

(1) Progression formulae

(2) Sum of 1st ‘n’ natural nos = ∑n = n(n+1)/2
Sum of the squares of 1st ‘n’ natural nos = ∑(n^2) = n (n+1) (2n+1) /6
Sum of the cubes of 1st ‘n’ natural nos = ∑(n^3) = [∑n]^2 = (n^2) [(2n+1)^2] / 4

(3) a,b,c are in arithmetic progression if b= (a+b)/2

(4) a,b,c are in harmonic progression if b= 2ac/ (a+c)

(5) If the terms of any progression is specified as a fuction f(x) then sum fo the progression series is given as
Sn = ∑(Tn) = ∑ [f(x)]
Eg: If terms of a progression series is given by the function f(x)