0580 P43 - Jun 2011 - Q11 - 14 marks
16344
(a)(i) Find the sum of the first 4 positive integers. [1]
The sum of the first n positive integers is \(n(n+1)/2\).
(a)(ii) Show this formula is correct when n = 3. [1]
(a)(iii) Find the sum of the first 120 positive integers. [1]
(a)(iv) Find 121 + 122 + … + 200. [2]
(a)(v) Find 2 + 4 + 6 + … + 800. [2]
| Cubes | Integers |
|---|---|
| \(1^3=1\) | \(1=1\) |
| \(1^3+2^3=9\) | \(1+2=3\) |
| \(1^3+2^3+3^3=\ldots\) | \(1+2+3=\ldots\) |
| \(1^3+2^3+3^3+4^3=\ldots\) | \(1+2+3+4=\ldots\) |
(b)(i) Complete the four blanks. [2]
(b)(ii) The first 14 integers sum to 105. Find the sum of the first 14 cubes. [1]
(b)(iii) Write a formula for the sum of the first n cubes. [1]
(b)(iv) Find the sum of the first 60 cubes. [1]
(b)(v) Find n when the sum of the first n cubes is 278784. [2]
