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)) nth term is an = a + nd where an is the nth term a is first term d is difference between terms 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 |