Alternative solution for problem involving consecutive numbers.

Problem: What numbers from 30 to 70 are the sum of two or more consecutive numbers?

I was able to answer it by simply trying out every number and testing it, and I got:

30 is the sum of all consecutive numbers from 4 to 8.

31 is the sum of all consecutive numbers from 15 to 16.

33 is the sum of all consecutive numbers from 3 to 8.

34 is the sum of all consecutive numbers from 7 to 10.

35 is the sum of all consecutive numbers from 2 to 8.

36 is the sum of all consecutive numbers from 1 to 8.

37 is the sum of all consecutive numbers from 18 to 19.

38 is the sum of all consecutive numbers from 8 to 11.

39 is the sum of all consecutive numbers from 4 to 9.

40 is the sum of all consecutive numbers from 6 to 10.

41 is the sum of all consecutive numbers from 20 to 21.

42 is the sum of all consecutive numbers from 3 to 9.

43 is the sum of all consecutive numbers from 21 to 22.

44 is the sum of all consecutive numbers from 2 to 9.

45 is the sum of all consecutive numbers from 1 to 9.

46 is the sum of all consecutive numbers from 10 to 13.

47 is the sum of all consecutive numbers from 23 to 24.

48 is the sum of all consecutive numbers from 15 to 17.

49 is the sum of all consecutive numbers from 4 to 10.

50 is the sum of all consecutive numbers from 8 to 12.

51 is the sum of all consecutive numbers from 6 to 11.

52 is the sum of all consecutive numbers from 3 to 10.

53 is the sum of all consecutive numbers from 26 to 27.

54 is the sum of all consecutive numbers from 2 to 10.

55 is the sum of all consecutive numbers from 1 to 10.

56 is the sum of all consecutive numbers from 5 to 11.

57 is the sum of all consecutive numbers from 7 to 12.

58 is the sum of all consecutive numbers from 13 to 16.

59 is the sum of all consecutive numbers from 29 to 30.

60 is the sum of all consecutive numbers from 4 to 11.

61 is the sum of all consecutive numbers from 30 to 31.

62 is the sum of all consecutive numbers from 14 to 17.

63 is the sum of all consecutive numbers from 3 to 11.

65 is the sum of all consecutive numbers from 2 to 11.

66 is the sum of all consecutive numbers from 1 to 11.

67 is the sum of all consecutive numbers from 33 to 34.

68 is the sum of all consecutive numbers from 5 to 12.

69 is the sum of all consecutive numbers from 9 to 14.

70 is the sum of all consecutive numbers from 7 to 13.

Since this is very tedious, I was wondering if there was any alternative solution for this.

Thanks.

Re: Alternative solution for problem involving consecutive numbers.

note ...

Re: Alternative solution for problem involving consecutive numbers.