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Sum Divisibility Dilemma (Posted on 2014-03-18) Difficulty: 3 of 5
Determine a general formula (in terms of n) for the sum of the first n positive integers that are not divisible by 5.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts solution | Comment 4 of 6 |

I see that the below "solution" misinterprets what is asked. It has the sum of the first n positive integers minus the multiples of 5:

n*(n+1)/2 - [n/5]*([n/5] + 1)*5/2

where [ ] represents the floor function.

To test it:

DEFDBL A-Z
CLS
FOR n = 1 TO 45
    PRINT n, n * (n + 1) / 2 - INT(n / 5) * (INT(n / 5) + 1) * 5 / 2
NEXT

n             sum
1             1
2             3
3             6
4             10
5             10
6             16
7             23
8             31
9             40
10            40
11            51
12            63
13            76
14            90
15            90
16            106
17            123
18            141
19            160
20            160
21            181
22            203
23            226
24            250
25            250
26            276
27            303
28            331
29            360
30            360
31            391
32            423
33            456
34            490
35            490
36            526
37            563
38            601
39            640
40            640
41            681
42            723
43            766
44            810
45            810

Edited on March 18, 2014, 3:19 pm
  Posted by Charlie on 2014-03-18 15:10:39

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