11X1 T14 06 sum of a geometric series (2011)

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<p> 1. Sum Of A Geometric Series 2. Sum Of A Geometric Series S n a ar ar 2 ar n1 3. Sum Of A Geometric Series S n a ar ar 2 ar n1rSn ar ar 2 ar 3 ar n1 ar n 4. Sum Of A Geometric Series S n a ar ar 2 ar n1rSn ar ar 2 ar 3 ar n1 ar n r 1Sn ar n a 5. Sum Of A Geometric Series S n a ar ar 2 ar n1rSn ar ar 2 ar 3 ar n1 ar n r 1Sn ar n a ar n 1Sn r 1 6. Sum Of A Geometric Series S n a ar ar 2 ar n1rSn ar ar 2 ar 3 ar n1 ar n r 1Sn ar n a ar n 1Sn , if r 1 r 1 7. Sum Of A Geometric Series S n a ar ar 2 ar n1rSn ar ar 2 ar 3 ar n1 ar n r 1Sn ar n a ar n 1Sn , if r 1 r 1OR a1 r n Sn 1 r 8. Sum Of A Geometric Series S n a ar ar 2 ar n1rSn ar ar 2 ar 3 ar n1 ar n r 1Sn ar n a ar n 1Sn , if r 1 r 1OR a1 r n , if r 1Sn 1 r 9. Sum To Infinity (Limiting Sum) 10. Sum To Infinity (Limiting Sum)NOTE : r 1 11. Sum To Infinity (Limiting Sum)NOTE : r 1If r 1, lim r n 0n 12. Sum To Infinity (Limiting Sum)NOTE : r 1If r 1, lim r n 0a1 r n nlim S n limn n 1 r 13. Sum To Infinity (Limiting Sum)NOTE : r 1If r 1, lim r n 0a1 r n nlim S n limn n 1 ra1 r 14. Sum To Infinity (Limiting Sum)NOTE : r 1If r 1, lim r n 0a1 r n nlim S n limn n 1 ra1 raS , if r 1 1 r 15. Sum To Infinity (Limiting Sum)NOTE : r 1 If r 1,lim r n 0a1 r n nlim S n limn n 1 ra1 raS , if r 1 1 re.g. i Find the sum of the first 10 terms of 2 6 18 16. Sum To Infinity (Limiting Sum)NOTE : r 1 If r 1,lim r n 0a1 r n nlim S n limn n 1 ra1 raS , if r 1 1 re.g. i Find the sum of the first 10 terms of 2 6 18 a 2, r 3 and n 10 17. Sum To Infinity (Limiting Sum)NOTE : r 1 If r 1,lim r n 0a1 r n nlim S n limn n 1 ra1 raS , if r 1 1 re.g. i Find the sum of the first 10 terms of 2 6 18 a 2, r 3 and n 10 ar n 1 Sn r 1 18. Sum To Infinity (Limiting Sum)NOTE : r 1 If r 1,lim r n 0a1 r n nlim S n limn n 1 ra1 raS , if r 1 1 re.g. i Find the sum of the first 10 terms of 2 6 18 a 2, r 3 and n 10 ar n 1 Sn r 12310 1S10 3 1 19. Sum To Infinity (Limiting Sum)NOTE : r 1 If r 1,lim r n 0a1 r n nlim S n limn n 1 ra1 raS , if r 1 1 re.g. i Find the sum of the first 10 terms of 2 6 18 a 2, r 3 and n 10 ar n 1 Sn r 12310 1S10 3 1 59048 20. n11 8ii 6 n3 2 21. n1 211 8ii 6 a 6 n3 2 2 22. n1 211 8ii 6 a 6 n3 2 232 23. n1 211 8 1ii 6 a 6 r ,n6n3 2 2232 24. n1 211 8 1ii 6 a 6 r ,n6n3 2 2232a1 r n Sn 1 r 25. n1 211 8 1ii 6 a 6 r ,n6n3 2 2233 1621 a1 r n 2 2 Sn S6 1 r 1 1 2 26. n1 211 8 1ii 6 a 6 r ,n6n3 2 223 3 1 62 1 a1 r n 2 2 Sn S6 1 r1123 63 2 2 64 1189 64 27. n1 211 8 1ii 6 a 6 r ,n6n3 2 2233 1621 a1 r n2 2 Sn S6 1 r1 1 2 3 63 2 2 64 1 189 642iii Does 56 4 have a limiting sum?7 28. n1 211 8 1ii 6 a 6 r ,n6n3 2 2233 1621 a1 r n2 2 Sn S6 1 r 1 1 2 3 63 2 2 64 1 189 642iii Does 56 4 have a limiting sum?74 r 1 56 29. n1 211 8 1ii 6 a 6 r ,n6n3 2 223 3 1 62 1 a1 r n 2 2 Sn S6 1 r1123 63 2 2 64 1189 64 2iii Does 56 4 have a limiting sum? 74 r 1 56 as r 1, it has a limiting sum 30. 1 1 1iv 2 4 8 31. 1 1 1iv 2 4 81 1 a ,r 2 2 32. a1 1 1iv S 2 4 81 r1 1 a ,r 2 2 33. a1 1 1iv S 2 4 81 r1 1 1 a ,r 2 2 2112 1 34. a1 1 1iv S 2 4 81 r1 1 1 a ,r 2 2 2112 1v Write 0.36 as a fraction 35. a1 1 1iv S 2 4 81 r1 1 1 a ,r 2 2 2112 1v Write 0.36 as a fraction 0.36 0.36 0.0036 0.000036 36. a1 1 1iv S 2 4 81 r1 1 1 a ,r 2 2 2112 1v Write 0.36 as a fraction 0.36 0.36 0.0036 0.000036 a 0.36, r 0.01 37. a1 1 1iv S 2 4 81 r1 1 1 a ,r 2 2 2112 1v Write 0.36 as a fraction 0.36 0.36 0.0036 0.000036 a 0.36, r 0.01a S 1 r 38. a1 1 1iv S 2 4 81 r1 1 1 a ,r 2 2 2112 1v Write 0.36 as a fraction 0.36 0.36 0.0036 0.000036 a 0.36, r 0.01 a S 1 r0.361 0.013699 411 39. a1 1 1iv S 2 4 81 r1 1 1 a ,r 2 2 2112Exercise 6J; 3cf, 5, 7b 1 8a(i), 9, 12, 14, 17bv Write 0.36 as a fraction 0.36 0.36 0.0036 0.000036 Exercise 6K; 2adgj, 3b,a 0.36, r 0.014a, 6bf, 8, 11a, 17ace, 19* a S 1 rExercise 6L, 1dg, 2d, 4a0.361 0.013699 411</p>