Содержание
- 2. Mathematical Induction Let Sn, n = 1,2,3,… be statements involving positive integer numbers n. Suppose that
- 3. for all positive integers n. If it is assumed that the sequence {xn} converges, then Question
- 4. Therefore, the principle of mathematical induction tells us that for any positive integer n. Our first
- 5. in both parts of the relationship But, what if this is a free-response question? Then we
- 6. Question 1: Answers to Questions from Light #2: Sequences and Limits Question 2: Question 4: Question
- 7. Calculus++ Also known as Hysterical Calculus
- 8. Question 1b. Find the limit of the sequence Solution. We have Using the equivalence we obtain
- 9. Using now the equivalence we obtain Therefore,
- 10. Question 2b. Find the following limit Solution. Actually, the equivalence gives an incorrect result for this
- 11. The last equivalence yields
- 12. Question 3. Find the following limit Solution. We have to find precise equivalent functions for each
- 13. A similar (but even more difficult) calculation yields Therefore and
- 14. Picture of the Week
- 15. Question 8. The initial location of a snail is the point S1 = (0,0). The first
- 16. a) Show that xn+3 + xn+2 + xn+1 + ½ xn = 2, and find a
- 17. Snail path in the xy – plane. y
- 18. Solution. Write down the characteristic equation for the formula Unfortunately, this equation has only two real
- 19. Therefore Thus If the sequence xn converges to , then Passing to the limit in the
- 20. Snail path in the xy – plane. y
- 22. Скачать презентацию