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Further Maths: Core Pure -Edexcel-A Level

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  1. complex-numbers-and-argand-diagrams
    6 主题
  2. exponential-form-and-de-moivres-theorem
    4 主题
  3. properties-of-matrices
    3 主题
  4. transformations-using-matrices
    3 主题
  5. roots-of-polynomials
    2 主题
  6. series
    2 主题
  7. maclaurin-series
    1 主题
  8. hyperbolic-functions
    4 主题
  9. volumes-of-revolution
    2 主题
  10. methods-in-calculus
    5 主题
  11. vector-lines
    4 主题
  12. vector-planes
    4 主题
  13. polar-coordinates
    2 主题
  14. first-order-differential-equations
    3 主题
  15. second-order-differential-equations
    2 主题
  16. simple-harmonic-motion
    2 主题
  17. proof-by-induction
    2 主题
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Method of differences

What is the method of differences?

  • The Method of Differences is a way of turning longer and more complicated sums into shorter and simpler ones

  • Sometimes when summing series, you will notice that many of the terms (or parts of the terms) simply “cancel out” or eliminate each other

    • This can turn a very long series summation, into a much simpler shorter one

  • In the case of sum from r equals 1 to n of left parenthesis f left parenthesis r right parenthesis minus f left parenthesis r plus 1 right parenthesis right parenthesis

    • f left parenthesis 1 right parenthesis minus f left parenthesis 2 right parenthesis

    • f left parenthesis 2 right parenthesis minus f left parenthesis 3 right parenthesis

    • <img alt=”f left parenthesis 3 right parenthesis minus f left parenthesis 4 right parenthesis” data-mathml='<math ><semantics><mrow><mi>f</mi><mo>(</mo><mn>3</mn><mo>)</mo><mo>-</mo><mi>f</mi><mo>(</mo><mn>4</mn><mo>)</mo></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″}</annotation></semantics></math>’ height=”22″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2222%22%20width%3D%2278%22%20wrs%3Abaseline%3D%2216%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ef%3C%2Fmi%3E%3Cmo%3E(%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmo%3E)%3C%2Fmo%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmi%3Ef%3C%2Fmi%3E%3Cmo%3E(%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmo%3E)%3C%2Fmo%3E%3C%2Fmath%3E–%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3E%40font-face%7Bfont-family%3A’math1da40657c9fece7e48d30af42d3’%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMi7iBBMAAADMAAAATmNtYXDEvmKUAAABHAAAADRjdnQgDVUNBwAAAVAAAAA6Z2x5ZoPi2VsAAAGMAAAAcmhlYWQQC2qxAAACAAAAADZoaGVhCGsXSAAAAjgAAAAkaG10eE2rRkcAAAJcAAAACGxvY2EAHTwYAAACZAAAAAxtYXhwBT0FPgAAAnAAAAAgbmFtZaBxlY4AAAKQAAABn3Bvc3QB9wD6AAAEMAAAACBwcmVwa1uragAABFAAAAAUAAADSwGQAAUAAAQABAAAAAAABAAEAAAAAAAAAQEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAgICAAAAAg1UADev96AAAD6ACWAAAAAAACAAEAAQAAABQAAwABAAAAFAAEACAAAAAEAAQAAQAAIhL%2F%2FwAAIhL%2F%2F93vAAEAAAAAAAABVAMsAIABAABWACoCWAIeAQ4BLAIsAFoBgAKAAKAA1ACAAAAAAAAAACsAVQCAAKsA1QEAASsABwAAAAIAVQAAAwADqwADAAcAADMRIRElIREhVQKr%2FasCAP4AA6v8VVUDAAABAIABVQLVAasAAwAwGAGwBBCxAAP2sAM8sQIH9bABPLEFA%2BYAsQAAExCxAAblsQABExCwATyxAwX1sAI8EyEVIYACVf2rAatWAAAAAQAAAAEAANV4zkFfDzz1AAMEAP%2F%2F%2F%2F%2FWOhNz%2F%2F%2F%2F%2F9Y6E3MAAP8gBIADqwAAAAoAAgABAAAAAAABAAAD6P9qAAAXcAAA%2F7YEgAABAAAAAAAAAAAAAAAAAAAAAgNSAFUDVgCAAAAAAAAAACgAAAByAAEAAAACAF4ABQAAAAAAAgCABAAAAAAABAAA3gAAAAAAAAAVAQIAAAAAAAAAAQASAAAAAAAAAAAAAgAOABIAAAAAAAAAAwAwACAAAAAAAAAABAASAFAAAAAAAAAABQAWAGIAAAAAAAAABgAJAHgAAAAAAAAACAAcAIEAAQAAAAAAAQASAAAAAQAAAAAAAgAOABIAAQAAAAAAAwAwACAAAQAAAAAABAAS

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