4.06a-b Summation of series and the method of differences Quiz: OCR Further Maths, Unit 1

The 20 questions

1. What is the closed-form expression for the sum of the first n positive integers?

   • n^2 / 2
   • n(n + 1)
   • n(n - 1) / 2
   • n(n + 1) / 2

2. What is the standard formula for the sum of the first n square numbers?

   • n(n + 1)(2n - 1) / 6
   • n(n + 1)(2n + 1) / 6
   • n^2(n + 1)^2 / 6
   • n(n - 1)(2n + 1) / 6

3. What is the standard formula for the sum of the first n cube numbers?

   • n^2(n + 1)^2 / 2
   • n^3(n + 1)^3 / 4
   • n^2(n + 1)^2 / 4
   • n(n + 1)(n + 2) / 4

4. What is the value of the sum of r squared from r equals 1 to 10?

   • 3025
   • 385
   • 330
   • 505

5. What is the value of the sum of r cubed from r equals 1 to 10?

   • 385
   • 3025
   • 2025
   • 3000

6. In the method of differences, what algebraic structure allows intermediate terms to cancel out?

   • Telescoping series
   • Binomial expansion
   • Geometric progression
   • Harmonic progression

7. Which expression represents 1 over r times r plus 1 in partial fraction form?

   • 1/(2r) - 1/(2r + 2)
   • 1/r - 1/(r + 1)
   • 1/(r + 1) - 1/r
   • 1/r + 1/(r + 1)

8. What is the sum of 1 over r times r plus 1 from r equals 1 to n?

   • 1 / (n + 1)
   • (n + 1) / n
   • n / (n + 1)
   • 1 - n

9. What is the sum to infinity of 1 over r times r plus 1 starting from 1?

   • 1/2
   • Infinity
   • 1
   • 0

10. Which partial fraction identity is correct for 1 over 2r minus 1 times 2r plus 1?

    • 1/2(1/(2r-1) + 1/(2r+1))
    • 1/(2r-1) - 1/(2r+1)
    • 1/(2r+1) - 1/(2r-1)
    • 1/2(1/(2r-1) - 1/(2r+1))

11. What is the sum from r equals 1 to n of 1 over (2r - 1)(2r + 1)?

    • 2n / (2n + 1)
    • n / (n + 1)
    • n / (2n + 1)
    • 1 / (2n + 1)

12. What is the sum to infinity of 1 over (2r - 1)(2r + 1) starting from r equals 1?

    • 0
    • 1/4
    • 1/2
    • 1

13. What is the simplified expression for the sum of the first n odd positive integers?

    • n(n + 1)
    • 2n - 1
    • 2n^2
    • n^2

14. What is the simplified expression for the sum of r times r plus 1 from 1 to n?

    • n(n + 1)(n + 2) / 3
    • n(n - 1)(n + 1) / 3
    • n(n + 1)(2n + 1) / 3
    • n(n + 1)(n + 2) / 6

15. What is the value of the sum of integers from r equals 11 to 20 inclusive?

    • 210
    • 165
    • 145
    • 155

16. Evaluating the sum from r equals 1 to n of f(r) minus f(r plus 1) gives which result?

    • f(n) - f(1)
    • f(1) - f(n)
    • f(n + 1) - f(1)
    • f(1) - f(n + 1)

17. In the telescoping sum of f(r + 2) minus f(r) from 1 to n, how many terms remain?

    • 2 terms
    • 1 term
    • n terms
    • 4 terms

18. What is the simplified expression for the sum of 3r plus 2 from r equals 1 to n?

    • n(3n + 5) / 2
    • n(3n + 7) / 2
    • 3n(n + 1) / 2
    • n(3n + 2)

19. What is the sum to infinity of 2 over r(r + 1)(r + 2) starting from r equals 1?

    • 1/2
    • 1
    • 1/4
    • 2

20. What is the value of the sum of 2r from r equals 1 to 50?

    • 2600
    • 2550
    • 2500
    • 1275

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