Series

Geometric Series is one where the ratio of successive terms in the
series is constant (r). a is the frist term.

a + ar + ar² + ar³ + ar⁴ + ...

Convergent, if –1>r>+1
Sum to infinity is S = a/(1 - r)

Sum of first n terms is
   S = a(1 – rⁿ)/(1 – r)

(1/2)+(1/4)+(1/8)+(1/16) ... = 1
(1/2)–(1/4)+(1/8)–(1/16) ... = 1/3

Arithmetic Series  is a sequence of numbers such that the
difference between the consecutive terms is constant.

a + (a+d) + (a+2d) + (a+3d) + ...

Sum of first n terms is
   S = (n/2)(a + an)
   S = (n/2)(2a+d(n–1))
   where an is the nth term

1 + 2 + 3 + 4 + ...
1 – 2 + 3 – 4 + ...


Sum the Integers from 1 to N inclusive
Sum = N(N+1)/2

from n to m inclusive
sum = (1/2)(m(m+1) – n(n+1))

Sum of first even integers
from 2 to N inclusive
Sum = N(N+1)
N = ((First Even + Last Even)/2) – 1
example, sum of 2+4+6+8+..+100
N = ((100+2)/2) – 1 = 50

Sum of first odd integers
from 1 to N inclusive
Sum = N²

Sum of first N digits separated by d
Sn = n/2(2a + (n-1)d)
a is first term
d is common diff


Taylor series
f(x) = f(a) + (f'(a)/1!)(x–a) + (f''(a)/2!)(x–a)^2 +
       (f'''(a)/3!)(x–a)^3 + ...

for sinx around 0
f(x) = 0 + (cos(0)/1)(x) – (sin(0)/2)(x)^2 –
       (cos(0)/6)(x)^3 + sin(0)/24)(x^4)...
f(x) = x – (x^3/3!) + (x^5/5!) – (x^7/7!)




Home

Area, Volume
Atomic Mass
Black Body Radiation
Boolean Algebra
Calculus
Capacitor
Center of Mass
Carnot Cycle
Charge
Chemistry
  Elements
  Reactions
Circuits
Complex numbers
Constants
Curves, lines
deciBell
Density
Electronics
Elements
Flow in fluids
Fourier's Law
Gases
Gravitation
Greek Alphabet
Horizon Distance
Interest
Magnetics
Math   Trig
Math, complex
Maxwell's Eq's
Motion
Newton's Laws
Octal/Hex Codes
Orbital Mechanics
Particles
Parts, Analog IC
  Digital IC   Discrete
Pendulum
Planets
Pressure
Prime Numbers
Questions
Radiation
Refraction
Relativistic Motion
Resistance, Resistivity
Rotation
Series
SI (metric) prefixes
Skin Effect
Specific Heat
Springs
Stellar magnitude
Thermal
Thermal Conductivity
Thermal Expansion
Thermodynamics
Trigonometry
Units, Conversions
Vectors
Volume, Area
Water
Wave Motion
Wire, Cu   Al   metric
Young's Modulus