This document contains solutions to math problems involving summations. It demonstrates how to calculate the sum of consecutive even or odd numbers using the formula S = n(n+1)/2 or S = n^2 respectively. Several examples are worked through step-by-step showing how to determine the upper limit and calculate the summation.

1. 1º DE SECUNDARIA
ÁREA : MATEMÁTICA
SEMANA 6
EXPERIENCIA 2
ACTIVIDAD 6
SUMATORIAS
DEMETRIO CCESA RAYME

2. 𝟐 + 𝟒 + 𝟔 + 𝟖 + ⋯ + 𝟐𝒏 = 𝒏(𝒏 + 𝟏)

3. S = 2 + 4 + 6 + ............ + 44
A) 406 B) 506 C) 552 D) 606

4. S = 2 + 4 + 6 + ............ + 44
A) 406 B) 506 C) 552 D) 606
S = 𝟐𝟐(𝟐𝟐 + 𝟏)= 22(𝟐𝟑)=506
2n = 44
n = 22
Solución

5. S = 2 + 4 + 6 + ............ + 82
A) 1712 B) 1722 C) 1732 D) 1742

6. S = 2 + 4 + 6 + ............ + 82
A) 1712 B) 1722 C) 1732 D) 1742
S = 𝟒𝟏(𝟒𝟏 + 𝟏)= 41(𝟒𝟐)=1722
2n = 82
n = 41
Solución

7. S = 2 + 4 + 6 + ............ + 66
A) 1056 B) 1116 C) 1122 D) 1126

8. S = 2 + 4 + 6 + ............ + 66
A) 1056 B) 1116 C) 1122 D) 1126
S = 𝟑𝟑(𝟑𝟑 + 𝟏)= 33(𝟑𝟒)=1122
2n = 66
n = 33
Solución

9. S = 2 + 4 + 6 + ............ + 222
A) 12412 B) 12422 C) 12432 D) 12442

10. 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

11. S = 10 + 12 + 14 + ............ + 66
A) 1021 B) 1102 C) 1122 D) 1022

12. S = 10 + 12 + 14 + ............ + 66
A) 1021 B) 1102 C) 1122 D) 1022
S = 𝟑𝟑(𝟑𝟑 + 𝟏)= 33(𝟑𝟒)=1122
2n = 66
n = 33
2n = 8
n = 4
S = 𝟒(𝟒 + 𝟏)= 4(𝟓)=20
S = 1122 – 20 = 1102
S = 2 + 4 + 6 + 8 + 10 + 12 + 14 + ............ + 66

13. S = 20 + 22 + 24 + ............ + 80
A) 1650 B) 1640 C) 1560 D) 1550

14. S = 20 + 22 + 24 + ............ + 80
A) 1650 B) 1640 C) 1560 D) 1550
S = 𝟒𝟎(𝟒𝟎 + 𝟏)= 40(𝟒𝟏)=1640
2n = 80
n = 40
2n = 18
n = 9
S = 𝟗(𝟗 + 𝟏)= 9(𝟏𝟎)=90
S = 1640 – 90 = 1550
S = 2 + 4 + 6 + ….. +18 + 20 + 22 + 24 + ........ + 80

15. S = 32 + 34 + 36 + ............ + 98
A) 2210 B) 2220 C) 2230 D) 2240

16. S = 32 + 34 + 36 + ............ + 98
A) 2210 B) 2220 C) 2230 D) 2240
S = 𝟒𝟗(𝟒𝟗 + 𝟏)= 49(𝟓𝟎)=2450
2n = 98
n = 49
2n = 30
n = 15
S = 𝟏𝟓(𝟏𝟓 + 𝟏)= 15(𝟏𝟔)=240
S = 2450 – 240 = 1550
S = 2 + 4 + 6 + ….. +30 + 32 + 34 + 36 + ........ + 98

17. S = 42 + 44 + 46 + ............ + 144
A) 4096 B) 4816 C) 4826 D) 4836

18. S = 42 + 44 + 46 + ............ + 144
A) 4096 B) 4816 C) 4826 D) 4836
S = 𝟕𝟐(𝟕𝟐 + 𝟏)= 72(𝟕𝟑)=5256
2n = 144
n = 72
2n = 40
n = 20
S = 𝟐𝟎(𝟐𝟎 + 𝟏)= 20(𝟐𝟏)=420
S = 5256 – 420 = 4836
S = 2 + 4 + 6 + ….. +40 + 42 + 44 + 46 + ........+ 144

19. S = 74 + 76 + 78 + ............ + 204
A) 9164 B) 9174 C) 9184 D) 9194

20. S = 74 + 76 + 78 + ............ + 204
A) 9164 B) 9174 C) 9184 D) 9194
S = 𝟏𝟎𝟐(𝟏𝟎𝟐 + 𝟏)= 102(𝟏𝟎𝟑)=10506
2n = 204
n = 102
2n = 72
n = 36
S = 𝟑𝟔(𝟑𝟔 + 𝟏)= 36(𝟑𝟕)=1332
S = 10506 – 1332 = 9174
S = 2 + 4 + 6 + ….. +72 + 42 + 44 + 46 + ........+ 204

21. 𝟏 + 𝟑 + 𝟓 + 𝟕 + ⋯ + 𝟐𝒏 − 𝟏 = 𝒏𝟐

22. S = 1 + 3 + 5 + ............ + 37
A) 324 B) 360 C) 361 D) 371

23. S = 1 + 3 + 5 + ............ + 37
A) 324 B) 360 C) 361 D) 371
2n – 1 = 37
2n = 38
n = 19
𝐒 = (𝟏𝟗)𝟐
= 𝟑𝟔𝟏
Solución

24. S = 1 + 3 + 5 + ............ + 51
A) 756 B) 765 C) 729 D) 676

25. S = 1 + 3 + 5 + ............ + 51
A) 756 B) 765 C) 729 D) 676
2n – 1 = 51
2n = 52
n = 26
𝐒 = (𝟐𝟔)𝟐
= 𝟔𝟕𝟔
Solución

26. S = 1 + 3 + 5 + ............ + 69
A) 1025 B) 1125 C) 1225 D) 1525

27. S = 1 + 3 + 5 + ............ + 69
A) 1025 B) 1125 C) 1225 D) 1525
2n – 1 = 69
2n = 70
n = 35
𝐒 = (𝟑𝟓)𝟐
= 𝟏𝟐𝟐5
Solución

28. S = 1 + 3 + 5 + ............ + 109
A) 3025 B) 3125 C) 3625 D) 4225

29. S = 1 + 3 + 5 + ............ + 109
A) 3025 B) 3125 C) 3625 D) 4225
2n – 1 = 109
2n = 110
n = 55
𝐒 = (𝟓𝟓)𝟐
= 𝟑𝟎𝟐5
Solución

30. S = 1 + 3 + 5 + ............ + 127
A) 3600 B) 3906 C) 4096 D) 4906

31. S = 1 + 3 + 5 + ............ + 127
A) 3600 B) 3906 C) 4096 D) 4906
2n – 1 = 127
2n = 128
n = 64
𝐒 = (𝟔𝟒)𝟐
= 𝟒𝟎𝟗𝟔
Solución

32. S = 19 + 21 + 23 + ............ + 49
A) 544 B) 554 C) 564 D) 574

33. S = 19 + 21 + 23 + ............ + 49
A) 544 B) 554 C) 564 D) 574
2n – 1 = 49
2n = 50
n = 25
S = (𝟐𝟓)𝟐
= 𝟔𝟐𝟓
2n – 1 = 17
2n = 18
n = 9
S = (𝟗)𝟐
= 𝟖𝟏
S = 625 – 81 = 544
S = 1 + 3 + 5 + ….. +17 + 19 + 21 + 23 + ........ + 49

34. S = 21 + 23 + 25 + ............ + 89
A) 1915 B) 1925 C) 1935 D) 1945

35. S = 21 + 23 + 25 + ............ + 89
A) 1915 B) 1925 C) 1935 D) 1945
2n – 1 = 89
2n = 90
n = 45
S = (𝟒𝟓)𝟐
= 𝟐𝟎𝟐𝟓
2n – 1 = 19
2n = 20
n = 10
S = (𝟏𝟎)𝟐
= 𝟏𝟎𝟎
S = 2025 – 100 = 1925
S = 1 + 3 + 5 + ….. +19 + 21 + 23 + 25 + ........ + 89

36. S = 25 + 27 + 29 + ............ + 89
A) 2881 B) 2818 C) 1881 D) 1871

37. S = 25 + 27 + 29 + ............ + 89
A) 2881 B) 2818 C) 1881 D) 1871
2n – 1 = 89
2n = 90
n = 45
S = (𝟒𝟓)𝟐
= 𝟐𝟎𝟐𝟓
2n – 1 = 23
2n = 24
n = 12
S = (𝟏𝟐)𝟐
= 𝟏𝟒𝟒
S = 2025 – 144 = 1881
S = 1 + 3 + 5 + ….. +23 + 25 + 27 + 29 + ........ + 89

38. S = 51 + 53 + 55 + ............ + 161
A) 5926 B) 5936 C) 5946 D) 5956

39. S = 51 + 53 + 55 + ............ + 161
A) 5926 B) 5936 C) 5946 D) 5956
2n – 1 = 161
2n = 162
n = 81
S = (𝟖𝟏)𝟐
= 𝟔𝟓𝟔𝟏
2n – 1 = 49
2n = 50
n = 25
S = (𝟐𝟓)𝟐
= 𝟔𝟐𝟓
S = 6561 – 625 = 5936
S = 1 + 3 + 5 + ….. +49 + 51 + 53 + 55 + ........+ 161