Ex. Express as a surd.
Let x be the value of the continued fraction ; then whence 2x^2+ 2x-7=0.
The continued fraction is equal to the positive root of this equation, and is therefore equal to .
EXAMPLES XLIII. b.
Express the following surds as continued fractions, and find the sixth convergent to each:
1. 3. 2. 5. 3. 6. 4. 8. 5. 11. 6. 13. 7. 14. 8. 22. 9. 2 3. 10. 4 2. 11. 3 5. 12. 4 10. 13. 1 21. 14. 1 33. 15. 6 5. 16. 7 11. 17. Find limits of the error when {268}{65} is taken for 17. 18. Find limits of the error when {916} {191} is taken for 23.
19. Find the first convergent to 101 that is correct to five places of decimals.
20. Find the first convergent to 15 that is correct to five places of decimals.
Express as a continued fraction the positive root of each of the following equations:
21. . 22. . 28. .
24. Express each root of as a continued fraction. 25. Find the value of . 26. Find the value of . 28. Find the value of .
27. Find the value of .
