Teoría y problemas de sumatorias i PS15 ccesa007
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The document contains examples of calculating sums (sumatorias) of sequential numbers using formulas. It provides the sums of different number sequences and asks students to identify the correct total sum. The answers are worked out step-by-step showing the use of formulas such as Σn(n+1)/2 and n^2 to calculate totals.
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Teoría y problemas de sumatorias i PS15 ccesa007
- 1. 1º DE SECUNDARIA ÁREA : MATEMÁTICA SEMANA 5 EXPERIENCIA 2 ACTIVIDAD 4 SUMATORIAS I DEMETRIO CCESA RAYME =
- 2. 𝟏 + 𝟐 + 𝟑 + ⋯ + 𝒏 = 𝒏(𝒏 + 𝟏) 𝟐
- 3. A) 105 B) 115 C) 120 D) 136 S = 1 +2 +3+4+5+6+7+8+9+10+11+12+13+14+15
- 4. A) 105 B) 115 C) 120 D) 136 S = 1 +2 +3+4+5+6+7+8+9+10+11+12+13+14+15 Solución S = 𝟏𝟓(𝟏𝟓+𝟏) 𝟐 = 𝟏𝟓(𝟏𝟔) 𝟐 =120
- 5. S = 1 + 2 + 3 + ............ + 57 A) 1655 B) 1654 C) 1653 D) 1652
- 6. S = 1 + 2 + 3 + ............ + 57 A) 1655 B) 1654 C) 1653 D) 1652 S = 𝟓𝟕(𝟓𝟕+𝟏) 𝟐 = 𝟓𝟕(𝟓𝟖) 𝟐 =1653 Solución
- 7. S = 1 + 2 + 3 + ............ + 89 A) 4005 B) 4050 C) 4500 D) 4675
- 8. S = 1 + 2 + 3 + ............ + 89 A) 4005 B) 4050 C) 4500 D) 4675 S = 𝟖𝟗(𝟖𝟗+𝟏) 𝟐 = 𝟖𝟗(𝟗𝟎) 𝟐 =4005 Solución
- 9. S = 1 + 2 + 3 + ............ + 100 A) 5500 B) 5550 C) 5050 D) 5150
- 10. S = 1 + 2 + 3 + ............ + 100 A) 5500 B) 5550 C) 5050 D) 5150 S = 𝟏𝟎𝟎(𝟏𝟎𝟎+𝟏) 𝟐 = 𝟏𝟎𝟎(𝟏𝟎𝟏) 𝟐 =5050 Solución
- 11. S = 1 + 2 + 3 + ............ + 179 A) 15110 B) 16110 C) 16210 D) 16310
- 12. S = 1 + 2 + 3 + ............ + 179 A) 15110 B) 16110 C) 16210 D) 16310 S = 𝟏𝟕𝟗(𝟏𝟕𝟗+𝟏) 𝟐 = 𝟏𝟕𝟗(𝟏𝟖𝟎) 𝟐 =16110 Solución
- 13. S = 1 + 2 + 3 + ............ + 666 A) 222444 B) 222333 C) 222222 D) 222111
- 14. S = 1 + 2 + 3 + ............ + 666 A) 222444 B) 222333 C) 222222 D) 222111 S = 𝟔𝟔𝟔(𝟔𝟔𝟔+𝟏) 𝟐 = 𝟔𝟔𝟔(𝟔𝟔𝟕) 𝟐 =222111 Solución
- 15. S = 20 + 21 + 22 + ............ + 60 A) 1520 B) 1590 C) 1640 D) 1710
- 16. S = 20 + 21 + 22 + ............ + 60 A) 1520 B) 1590 C) 1640 D) 1710 S = 𝟔𝟎(𝟔𝟎+𝟏) 𝟐 = 𝟔𝟎(𝟔𝟏) 𝟐 =1830 S = 𝟏𝟗(𝟏𝟗+𝟏) 𝟐 = 𝟏𝟗(𝟐𝟎) 𝟐 =190 S = 1830 – 190 = 1640 S =1 + 2 + 3 +…..+19 + 20 + 21 + 22 + ............ + 60 TODO PARTE
- 17. S = 25 + 26 + 27 + ............ + 199 A) 16600 B) 16900 C) 17900 D) 19900
- 18. S = 25 + 26 + 27 + ............ + 199 A) 16600 B) 16900 C) 19600 D) 19900 S = 𝟏𝟗𝟗(𝟏𝟗𝟗+𝟏) 𝟐 = 𝟏𝟗𝟗(𝟐𝟎𝟎) 𝟐 =19900 S = 𝟐𝟒(𝟐𝟒+𝟏) 𝟐 = 𝟐𝟒(𝟐𝟓) 𝟐 =300 S = 19900 – 300 = 19600 S =1 + 2 + 3 +…..+24 + 25 + 26 + 27 + ........... + 199 TODO PARTE
- 19. S = 51 + 52 + 53 + ............ + 205 A) 19830 B) 19840 C) 19850 D) 19860
- 20. S = 51 + 52 + 53 + ............ + 205 A) 19830 B) 19840 C) 19850 D) 19860 S = 𝟐𝟎𝟓(𝟐𝟎𝟓+𝟏) 𝟐 = 𝟐𝟎𝟓(𝟐𝟎𝟔) 𝟐 =21115 S = 𝟓𝟎(𝟓𝟎+𝟏) 𝟐 = 𝟓𝟎(𝟓𝟏) 𝟐 =1275 S = 21115 – 1275 = 19840 S =1 + 2 + 3 +…..+50 + 51 + 52 + 53 + ........... + 205 TODO PARTE
- 21. S = 26 + 27 + 28 + ............ + 222 A) 24228 B) 24328 C) 24428 D) 24528
- 22. S = 26 + 27 + 28 + ............ + 222 A) 24228 B) 24328 C) 24428 D) 24528 S = 𝟐𝟐𝟐(𝟐𝟐𝟐+𝟏) 𝟐 = 𝟐𝟐𝟐(𝟐𝟐𝟑) 𝟐 =24753 S = 𝟐𝟓(𝟐𝟓+𝟏) 𝟐 = 𝟐𝟓(𝟐𝟔) 𝟐 =325 S = 24753 – 325 = 24428 S =1 + 2 + 3 +…..+25 + 26 + 27 + 28 + ........... + 222 TODO PARTE
- 23. S = 37 + 38 + 39 + ............ + 234 A) 26729 B) 26829 C) 26929 D) 26939
- 24. S = 37 + 38 + 39 + ............ + 234 A) 26729 B) 26829 C) 26929 D) 26939 S = 𝟐𝟑𝟒(𝟐𝟑𝟒+𝟏) 𝟐 = 𝟐𝟑𝟒(𝟐𝟑𝟓) 𝟐 =27495 S = 𝟑𝟔(𝟑𝟔+𝟏) 𝟐 = 𝟑𝟔(𝟑𝟕) 𝟐 =666 S = 27495 – 666 = 26829 S =1 + 2 + 3 +…..+36 + 37 + 38 + 39 + ........... + 234 TODO PARTE
- 25. 𝟐 + 𝟒 + 𝟔 + 𝟖 + ⋯ + 𝟐𝒏 = 𝒏(𝒏 + 𝟏)
- 26. S = 2 + 4 + 6 + ............ + 64 A) 1506 B) 1056 C) 1605 D) 1606
- 27. S = 2 + 4 + 6 + ............ + 64 A) 1506 B) 1056 C) 1605 D) 1606 S = 𝟑𝟐(𝟑𝟐 + 𝟏)= 32(𝟑𝟑)=1056 2n = 64 n = 32 Solución
- 28. S = 2 + 4 + 6 + ............ + 156 A) 6162 B) 6172 C) 6182 D) 6192
- 29. S = 2 + 4 + 6 + ............ + 156 A) 6162 B) 6172 C) 6182 D) 6192 S = 𝟕𝟖(𝟕𝟖 + 𝟏)= 78(𝟕𝟗)=6162 2n = 156 n = 78 Solución
- 30. S = 2 + 4 + 6 + ............ + 222 A) 12412 B) 12422 C) 12432 D) 12442
- 31. S = 2 + 4 + 6 + ............ + 222 A) 12412 B) 12422 C) 12432 D) 12442 S = 𝟏𝟏𝟏(𝟏𝟏𝟏 + 𝟏)= 111(𝟏𝟏𝟐)=12432 2n = 222 n = 111 Solución
- 32. S = 2 + 4 + 6 + ............ + 432 A) 46872 B) 46772 C) 46672 D) 46572
- 33. S = 2 + 4 + 6 + ............ + 432 A) 46872 B) 46772 C) 46672 D) 46572 S = 𝟐𝟏𝟔(𝟐𝟏𝟔 + 𝟏)= 216(𝟐𝟏𝟕)=46872 2n = 432 n = 216 Solución
- 34. S = 10 + 12 + 14 + ............ + 66 A) 1021 B) 1102 C) 1122 D) 1022
- 35. S = 10 + 12 + 14 + ............ + 66 A) 1021 B) 1102 C) 1122 D) 1022 S =2 + 4 + 6 + 8 + 10 + 12 + 14 + ............ + 66 2n = 8 n = 4 2n = 66 n = 33 S = 𝟑𝟑(𝟑𝟑 + 𝟏)= 33(𝟑𝟒)=1122 S = 𝟒(𝟒 + 𝟏)= 4(𝟓)=20 S = 1122 – 20 = 1102
- 36. S = 24 + 26 + 28 + ............ + 198 A) 9768 B) 9758 C) 9748 D) 9738
- 37. S = 24 + 26 + 28 + ............ + 198 A) 9768 B) 9758 C) 9748 D) 9738 2n = 22 n = 11 2n = 198 n = 99 S = 𝟗𝟗(𝟗𝟗 + 𝟏)= 99(𝟏𝟎𝟎)=9900 S = 𝟏𝟏(𝟏𝟏 + 𝟏)= 11(𝟏𝟐)=132 S = 9900 – 132 = 9768 S =2 + 4 + 6 +…..+22 + 24 + 26 + 28 + ........... +198
- 38. S = 42 + 44 + 46 + ............ + 144 A) 4096 B) 4816 C) 4826 D) 4836
- 39. S = 42 + 44 + 46 + ............ + 144 A) 4096 B) 4816 C) 4826 D) 4836 2n = 40 n = 20 2n = 144 n = 72 S = 𝟕𝟐(𝟕𝟐 + 𝟏)= 72(𝟕𝟑)=5256 S = 𝟐𝟎(𝟐𝟎 + 𝟏)= 20(𝟐𝟏)=420 S = 5256 – 420 = 4836 S =2 + 4 + 6 +…..+40 + 42 + 44 + 46 + ........... +144
- 40. S = 74 + 76 + 78 + ............ + 204 A) 9104 B) 9174 C) 9184 D) 9304
- 41. S = 74 + 76 + 78 + ............ + 204 A) 9104 B) 9174 C) 9184 D) 9304 2n = 72 n = 36 2n = 204 n = 102 S = 𝟏𝟎𝟐(𝟏𝟎𝟐 + 𝟏)= 102(𝟏𝟎𝟑)=10506 S = 𝟑𝟔(𝟑𝟔 + 𝟏)= 36(𝟑𝟕)=1332 S = 10506 – 1332 = 9174 S =2 + 4 + 6 +…..+72 + 74 + 76 + 78 + ........... +204
- 42. 𝟏 + 𝟑 + 𝟓 + 𝟕 + ⋯ + 𝟐𝒏 − 𝟏 = 𝒏𝟐
- 43. S = 1 + 3 + 5 + ............ + 51 A) 756 B) 765 C) 676 D) 729
- 44. S = 1 + 3 + 5 + ............ + 51 A) 756 B) 765 C) 676 D) 729 2n – 1 = 51 2n = 52 n = 26 𝐒 = (𝟐𝟔)𝟐 = 𝟔𝟕𝟔 Solución
- 45. S = 1 + 3 + 5 + ............ + 127 A) 3600 B) 3906 C) 3969 D) 4096
- 46. S = 1 + 3 + 5 + ............ + 127 A) 3600 B) 3906 C) 3969 D) 4096 2n – 1 = 127 2n = 128 n = 64 𝐒 = (𝟔𝟒)𝟐 = 𝟒𝟎𝟗𝟔 Solución
- 47. S = 25 + 27 + 29 + ............ + 109 A) 2881 B) 2882 C) 2883 D) 2884
- 48. S = 25 + 27 + 29 + ............ + 109 A) 2881 B) 2882 C) 2883 D) 2884 2n – 1 = 23 2n = 24 n = 12 S = (𝟏𝟐)𝟐 = 𝟏𝟒𝟒 2n – 1 = 109 2n = 110 n = 55 S = (𝟓𝟓)𝟐 = 𝟑𝟎𝟐𝟓 S = 3025 – 144 = 2881 S =1 + 3 + 5 +…..+23 + 25 + 27 + 29 + .......... + 109
- 49. S = 51 + 53 + 55 + ............ + 161 A) 5926 B) 5936 C) 5946 D) 5956
- 50. S = 51 + 53 + 55 + ............ + 161 A) 5926 B) 5936 C) 5946 D) 5956 2n – 1 = 49 2n = 50 n = 25 S = (𝟐𝟓)𝟐 = 𝟔𝟐𝟓 2n – 1 = 161 2n = 162 n = 81 S = (𝟖𝟏)𝟐 = 𝟔𝟓𝟔𝟏 S = 6561 – 625 = 5936 S =1 + 3 + 5 +…..+49 + 51 + 53 + 55 + .......... + 161