SOLUTION: How many numbers from 1 to 100 (inclusive) can be written as the sum of 2+ consecutive positive integers?

Question 229040: How many numbers from 1 to 100 (inclusive) can be written as the sum of 2+ consecutive positive integers?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Here are all of the numbers I could think of

1+2=3
2+3=5
1+2+3=6
3+4=7
4+5=9
1+2+3+4=10
5+6=11
3+4+5=12
6+7=13
2+3+4+5=14
7+8=15
8+9=17
5+6+7=18
9+10=19
2+3+4+5+6=20
10+11=21
4+5+6+7=22
11+12=23
7+8+9=24
12+13=25
5+6+7+8=26
13+14=27
1+2+3+4+5+6+7=28
14+15=29
9+10+11=30
15+16=31
16+17=33
7+8+9+10=34
17+18=35
11+12+13=36
18+19=37
8+9+10+11=38
19+20=39
6+7+8+9+10=40
20+21=41
13+14+15=42
21+22=43
2+3+4+5+6+7+8+9=44
22+23=45
10+11+12+13=46
23+24=47
15+16+17=48
24+25=49
11+12+13+14=50
25+26=51
3+4+5+6+7+8+9+10=52
26+27=53
17+18+19=54
27+28=55
5+6+7+8+9+10+11=56
28+29=57
13+14+15+16=58
29+30=59
19+20+21=60
30+31=61
14+15+16+17=62
31+32=63
32+33=65
21+22+23=66
33+34=67
5+6+7+8+9+10+11+12=68
34+35=69
16+17+18+19=70
35+36=71
23+24+25=72
36+37=73
17+18+19+20=74
37+38=75
6+7+8+9+10+11+12+13=76
38+39=77
25+26+27=78
39+40=79
14+15+16+17+18=80
40+41=81
19+20+21+22=82
41+42=83
27+28+29=84
42+43=85
20+21+22+23=86
43+44=87
3+4+5+6+7+8+9+10+11+12+13=88
44+45=89
29+30+31=90
45+46=91
8+9+10+11+12+13+14+15=92
46+47=93
22+23+24+25=94
47+48=95
31+32+33=96
48+49=97
23+24+25+26=98
49+50=99
18+19+20+21+22=100

Simply counting, I get 93 different numbers. So there are 93 different numbers that can be written as the sum of 2 or more consecutive positive integers (assuming I'm not forgetting anything).
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