Method of differences with partial fractions

Method of differences with partial fractions Quiz

Spec D4 · AQA A-Level Further Maths: Quiz

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  1. 1. Which is the partial fraction form of 1r(r+3)\frac{1}{r(r+3)}?

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

  2. 2. Find ∑r=1n[1r+1−1r+2]\sum_{r=1}^{n}\left[\frac{1}{r+1}-\frac{1}{r+2}\right].

    • A. 12−1n+1\frac12-\frac1{n+1}
    • B. 12−1n+2\frac12-\frac{1}{n+2}
    • C. 1−1n+21-\frac1{n+2}
    • D. 1n+2−12\frac{1}{n+2}-\frac12

  3. 3. What is ∑r=1∞1r(r+1)\sum_{r=1}^{\infty}\frac{1}{r(r+1)}?

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

  4. 4. Which terms remain in ∑r=1n[1r−1r+2]\sum_{r=1}^{n}\left[\frac1r-\frac1{r+2}\right]?

    • A. 1−1n+21-\frac{1}{n+2}
    • B. 1+12−1n+1−1n+21+\frac12-\frac1{n+1}-\frac1{n+2}
    • C. 12−1n+1\frac12-\frac1{n+1}
    • D. 1+12−1n−1n+11+\frac12-\frac1{n}-\frac{1}{n+1}

  5. 5. Given Sn=nn+1S_n=\frac{n}{n+1}, find ∑r=610ur\sum_{r=6}^{10}u_r.

    • A. 1011−67\frac{10}{11}-\frac{6}{7}
    • B. 1011−78\frac{10}{11}-\frac{7}{8}
    • C. 1011−56\frac{10}{11}-\frac{5}{6}
    • D. 1011−16\frac{10}{11}-\frac{1}{6}

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