9. What is the greatest number of terms for which the series [tex]\sum_{k=1}^n(k+1)[/tex] will have a value less than 65?

10. Calculate [tex]\frac{3+6+9+\ldots+402}{2+4+6+\ldots+402}[/tex].

11.
(a) Calculate [tex]\sum_{i=1}^{10} 1[/tex].

(b) Calculate [tex]\sum_{i=1}^{50} 1[/tex].

(c) Hence show that [tex]\sum_{n=1}^n 1 = n[/tex].

12. An athlete trains by running 600 meters on the first day, 900 meters on the second, 1200 meters on the third, and so forth.

(a) How far does he run on the 15th day?

(b) What is the total distance that he will run in 15 days?

(c) How long will it be before he can run a marathon of 42 km?

13. Shaun can do 27 push-ups per minute. Each week he improves his performance by 3 push-ups per minute. Mpho can do 20 push-ups per minute, and he increases his performance by 4 push-ups per minute each week.

(a) How many push-ups will they each do per minute in the fitness competition, which is in 10 weeks' time?

(b) After how many weeks will their number of push-ups per minute be the same?

(c) While training for the competition, Shaun spent 45 minutes doing push-ups per week. How many push-ups does he do altogether in the 10 weeks?

14. A ladder has 50 rungs. The bottom rung is 1 meter long. Each rung is 12.5 mm shorter than the rung beneath it. Determine the total length of wood required to make 50 rungs.