The method of differences

The method of differences Quiz

Spec 2.1 · Edexcel International A Level Further Maths: Quiz

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5 questions, one answer each

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  1. 1. What is ∑r=1n(1r−1r+1)\sum_{r=1}^{n}\left(\frac1r-\frac1{r+1}\right)?

    • A. 1n+1\frac{1}{n+1}
    • B. 1−1n+11-\frac{1}{n+1}
    • C. 1+1n+11+\frac{1}{n+1}
    • D. 1n−1n+1\frac1n-\frac{1}{n+1}

  2. 2. Find ∑r=1∞1r(r+1)\sum_{r=1}^{\infty}\frac{1}{r(r+1)}.

    • A. 12\frac12
    • B. 22
    • C. ∞\infty
    • D. 11

  3. 3. 1r(r+3)\frac{1}{r(r+3)} in partial fractions is

    • A. 13(1r−1r+3)\frac13\left(\frac1r-\frac1{r+3}\right)
    • B. 1r−1r+3\frac1r-\frac1{r+3}
    • C. 3(1r−1r+3)3\left(\frac1r-\frac1{r+3}\right)
    • D. 13(1r+1r+3)\frac13\left(\frac1r+\frac1{r+3}\right)

  4. 4. ∑r=14r⋅r!\sum_{r=1}^{4}r\cdot r! equals

    • A. 120120
    • B. 2424
    • C. 119119
    • D. 5!+15!+1

  5. 5. In ∑r=1n12(1r−1r+2)\sum_{r=1}^{n}\frac12\left(\frac1r-\frac1{r+2}\right), which terms do NOT cancel?

    • A. 1n+2\frac1{n+2} only
    • B. 11\frac11 only
    • C. 11,12,1n+1,1n+2\frac11,\frac12,\frac1{n+1},\frac1{n+2}
    • D. None

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